In the US, the taxpayer provides them like they provide roads. Rather unusual, because the American way is normally for the taxpayer to provide less rather than more.
That's true and there's a reason for it. Building and operating airports as transportation infrastructure fits within the US Constitutional guidance and constraints of "provide for the common defense, promote the general welfare". The word promote (as opposed to provide) was chosen to mean that the Federal Gubmint building domestic infrastructure is constitutional, directly giving people stuff other than that required to promote their own activity is not. The role of the US Federal Government was fairly precisely defined.
Not much of an admin problem for you Peter, because (reading your articles) you appear to have conquered most of it! But I have to say, reading all that stuff about how to make things happen in Europe often has me wondering whether it'll be worth the hassle!
But you're absolutely right about a lack of GA-accessible airports with decent opening hours. The trouble is, such airports aren't really commercially viable. In the US, the taxpayer provides them like they provide roads. Rather unusual, because the American way is normally for the taxpayer to provide less rather than more.
To argue slightly to the contrary, I don't see a huge "admin" problem with flying across Europe. Sure it isn't anything like as simple as in the USA, but with an IR, route planning software, and a means of getting mobile internet (which has to be a de facto requirement in the USA too - do serious pilots really phone up 1-800-WX-BRIEF and try to make sense of a verbal wx/notam briefing?) the planning takes a very short time.
Actually I think the worst time for flying across Europe was between somewhere before I started flying (2000) and about 2008, when Eurocontrol were chucking out flight plans for any of 10,000 reasons (of which about 5,000 change daily) but there was no way to develop routes. If you were an anorak and read the SRD documents, you had a start, but even then you got beaten by the daily CRAM. I was doing IR training in 2005 and one could spend hours on it, banging routes on an Italian flight simmer site. Finally Christof Edel beat in in 2008 with Autoplan (a now dead product) and that changed everything.
So planning is not hard. One is limited only by the aircraft capability versus the weather (just like in the USA) and then... well... by needing somewhere to land 
And the last bit is the biggest hurdle by far. There aren't enough GA-accessible airports with useful opening hours.
The European way of regulating is to approve organisations not individuals even if this creates systems like ISO9000 which anybody can operate as anything from useful to (the most common by far) complete utter sham. However EASA Part M is perceived to be a bigger meal than it is once you have good contacts. Sure the system wastes money like there was no tomorrow, and supports (much more effectively than the US system) firms who do a lousy job but who have "the right approvals" but the cost to the aircraft owner is generally much less than the cost of avgas flying somewhere. Obviously if you fly 30hrs a year then the opposite will be true...
Aircraft ownership is largely a "relationship game" and a "knowledge game", where if you don't know anybody decent (and have no contacts who can recommend someone) and don't know what the job involves then you are very likely to get shafted.
But that applies to everything else in life. If you randomly pick a lawyer and you yourself know little about what is involved, there is a very good chance you will get a crap job done. I am sure lawyers, indeed most professions, dislike customers who spend an hour on google before they visit With aviation it takes rather more than an hour to get clued up...
What we need most is usable airports, and an accessible IR.
Silvaire is right on the mark of course, as usual, which is why I am staying on the N-reg. EASA has not proposed any long term parking controls, and keeping 2 sets of pilot papers going is worth it.
If regulatory oversight focused more on assuring good decision making skills for pilots, owners and maintainers (who might be one and the same), planes would be better maintained, and more economical to operate.
That is the reality that many (but not all) regulators don't want to see, and is absolutely true. I think the regulators primary motivation in not understanding the issue is that licensing organisations instead of certificating people creates less work for them and consolidates the number of sources for government funding. It also hides some of the taxes from the consumer. Probably the biggest reason the FAA system has remained as flexible and effective as it has, is that funding is not directly extracted from the pilot, owner, or the businesses serving them. The net result is better efficiency and a decrease in overhead that adds no value.
Reading Piperboy84's attachment on owner self maintenance, I am reminded about some issues with the FAA Light Sport Category, in which the FAA has created an aircraft category similar to some of the microlight categories in European countries. This allows for a theoretical simplification of maintenance procedures but with one huge problem: the aircraft owner is tied to the manufacturer for parts and "support". That is not normally the case on N-register. Given that many owners of N-registered aircraft have a very cooperative and productive relationship with their mechanic, the theoretical benefits become just that, and the hard limits on parts sourcing look like a bigger problem for long term service. People have continued to choose older certified aircraft or experimental/homebuilts instead, because they are simpler and cheaper to maintain long term. The 'old' system works.
My response to the original question would be to say that the biggest limit on European GA is that the regulatory system looks out for itself, its jobs and its funding, as its primary role. The second biggest issue is the many languages in Europe, plus customs procedures and cross-border flight plan requirements that are much harder by plane than by car. If it were not for those factors, I think GA could be the same very useful tool for ~500-1000nm to destination business & personal trips as it is in the US. Its as easy in the US to make business trips of that length commercially as it is in Europe (flying being the best way in either case), but still people choose to fly themselves for the flexibility. Personal transportation by GA is similar: friends of mine have a small second house about 1000nm from their US home, and fly their C182 there a couple of times a year with no (government) flight plan, no PPR etc, just get in and go. Flexibility, which I find to be generally a less valued commodity in Europe, is the practical advantage of GA... without it, GA has nothing.
My big "fish to fry" is maintenance and modification centered. The staff of the national authority (pick your country) are trying to do the job the best they know how. However, natural attrition results in changes in the base skill sets of those staff members. Where the aircraft in consideration, the staff can be less than ideally prepared to appropriately deal with requests or required actions relative to these aircraft types. The result can, and usually is, "follow the process for this".
Well the process taken literally, and then to its most extreme or restrictive, can invoke a huge burden on the light aircraft owner/operator, which is simply not appropriate to that class/age/simplicity of aircraft. This results in requirements for maintenance programs, very involved justification for repair methods chosen, and requirements for "approval" of replacement parts, which may well be "next generation" and vastly improved.
The mis-aligned skill and experience base of the staff of the authority, coupled with the requirement for a risk analysis, and then conservatism which can naturally exist when a person is required to do something with which they are not familiar can make a simple task huge.
The result is that the owner/operator, who often has the wealth of experience to know better, and know what is appropriate to maintain the aircraft suitably airworthy (or at least access to that experience), can still be held back. When maintenance is held back this way, aircraft are less airworthy.
In Canada, the "Owner Maintenance" category was introduced many years ago. Though it still requires proper maintenance of aircraft, and is not a free for all of modify what you want, it does allow a lower threshold of "airworthy". "Airworthy" still requires "safe for flight", but "in compliance with the type design" has some wiggle room. Amusingly, the OM category had some of it's foundation in that it was widely known that Seabee owners where keeping their otherwise unsupported Franklin engines running by installing General Motors car engine valves. Apparently a certain part number was a direct fit replacement - perfect!
Sadly, the Seabee is one of the very few constant speed retractables allowed into this category (and mt Teal :) is another!). Thus many very worthy aircraft remain excluded from this streamlined path for maintenance - and aircraft are often less airworthy as a result.
The GA nations of the world need to ask themselves if they really want to be in the business of regulating the maintenance of private GA aircraft with the great intensity they do now. If regulatory oversight focused more on assuring good decision making skills for pilots, owners and maintainers (who might be one and the same), planes would be better maintained, and more economical to operate
Again, To add one point to Silvaire's post above, here is a list of what you can legally do yourself on a N reg plane
[mod - links fixed]
To add one point to Silvaire's post above, under the N-register part 91 there is no requirement for a CAMO; I look after maintenance scheduling for the King Air I fly and that saves us over £5k + VAT per year!
So, for all us ignoramus's out there, why is it G reg maintenance is so much more draconian and costly than N reg equivalent? Presumably there is little significant difference in observed safety between the two regimes.
Here are some reasons applicable to privately operated aircraft, I may have missed some.
I believe the safety record for N-register is slightly better, probably because of European weather issues and the inaccessibility of an IFR rating in the EU.
Public Image:
The average member of the public’s view that GA is an elitist rich boys sport. I think conveying the message to them that this is definitely not the case, in fact a significant percentage of the GA craft they see in the air are regular folks training for careers in air transport that will eventually fly people and freight as an important part of the nations economy. In the US the GA community really promote the image of GA doing good deeds and making a difference in the general public’s lives, groups such as Angels Flight (transporting medical patients and there family’s for free) and the Civil Air Patrol (doing S&R not just for other aircraft but for the members of the public in difficulties in remote areas) and the EAA Young Eagle program.
Another issue that adds to the image of GA being inaccessible and remote from the public is that since 911 enhanced airfield securities has made up close and personal access to planes and pilots significantly harder for the public. A guy would have difficulty taking is kid to the local airfield and having access to walk over and see the planes and talk to the pilots.
Not sure of the solution, but I think these are definitely issues that can cause the public to support or be indifferent to laws and regulations that stymie GA.
Over regulation of private and recreational flying! We need to fry ourselves for not acting as a vociferous, unified and organized voice to stop it!
