Apart from putting your Experimental on the European registry of choice (Sweden is popular here), there is no problem having them on US registry. Just this year there was some excitement about the CAA not extending the yearly permit to fly for US Experimentals but it got sorted out just in time. I've seen a lot of Experimentals on German registry, recently an immaculate Velocity XL RG.
I don't think the rules on Experimentals make it much harder for Europeans. The big exception might be IFR. There is currently no way to get approval for IFR in an Experimental but this might change over time.
Most do-it-yourself people have long since migrated to the microlight sector. I think Europe can compete with the US when it comes to small plane innovation it's just that it's mostly limited to the microlight sector because of the regulations.
There is a huge variation around Europe in how useful GA is.
The biggest-activity areas by far are UK and Germany, followed by France (depending on how one defines activity). The rest of Europe is much smaller. At the end you have countries with 100-200 aircraft; Greece for example has about 200, I believe.
But UK, Germany and France have good public transport and good roads.
If you lived in say Croatia or Greece, and owned a plane, then you get tremendous utility value (comparing to alternative transport). Especially in Greece, with all the islands which take for ever to get to by ferry. But in Greece it better be burning avtur - unless you base at one of the few avgas airports (Corfu, Megara, Athens, Sitia, Samos, not a lot more) or keep drums. But these places do not have much work/business in the outlying areas.
What works well in N Europe is a helicopter 
Add to that the very intense airliner traffic making for very congested airspace, even as low as FL60 or so
Where have you found that?
I've seen a lot of Experimentals on German registry, recently an immaculate Velocity XL RG.
There is a "process" for putting a US Exp aircraft onto the UK permit regime, but (not my area of expertise) most of the "dream planes" like the turbine Lancairs would be too hard or impossible. I don't know why but virtually nobody has achieved it.
Maybe, with no overt IFR capability, the payoff is too small.
And talking of low-end homebuilts, is there really a lot to gain in putting US-only-origin ones onto a European register? There is a big choice of them here already.
The stuff to go for would be the high performance types, and they are crippled by the lack of IFR.
As of 2011, there are some 547 airports served by the airlines and 19,784 total airports, of which 5172 are public use.
Germany has about 550 public airfields which is about 10% of what you quoted. The USA are about 27 times the size of Germany and about 3.75 times the population. So despite all complaints, we do have quite a bit of infrastructure still.
The fuel taxes which are included in the fuel price are the only contribution we have to pay for receiving ATC or FSS services. There are no overflight fees and no flightplan fees.
Fingers crossed that it will remain that way in the US. Airway fees in Europe start at 2 tons and IFR only. There are no flightplan fees.
We don't need to have a radio operators license and our pilot certificates do not expire. We require an flight review every two years that is administered by a CFI, you have to pass it but you can't fail it. Instrument privileges require 6 approaches, a hold, navigating by electronic means within a six month period. We can have a safety pilot sit in the right seat and reestablish currency if it has lapsed as long as the lapse hasn't extended another 6 months since we were last current. If it does, we have to fly with a CFII who conducts an Instrument Proficiency Check and we are back in business.
All available to Europeans by going N-reg and FAA license. About 30% of all aircraft in Germany are N-reg. EASA just made it harder by requiring an EASA license in addition to the FAA license but at the same time they are working on making the IR much more accessible. It seems they have realized that they have to be competitive with the FAA. Wish us luck.
We aren't mandated to have a 406 ELT or a mode S transponder.
Those are very good examples of really stupid regulation. Mainly the fault of our incompetent and unorganized lobby organizations. It appears they are slowly starting to get smarter in Cologne. The next expensive thing is 8.33kHz and then P-RNAV. Let's see what happens.
Those are very good examples of really stupid regulation
The ELT requirement is actually ICAO. What happened is that Europe did not mandate it for a long time.
Whether one thinks there is any point is another matter. I have one, and carry two portable ones (one old, one newer)
Mode S is a cockup.
8.33 is not too bad so long as - if they mandate it down to the surface - they keep it for IFR only, because all the GNS boxes, and later, are 8.33. Currently it is mandatory for FL200+.
PRNAV could be a killer for IFR GA... and a big moneyspinner for Garmin whose new boxes come with an EASA AML STC with all the stuff There is always a winner!
I've not been to Greece, but I can imagine an aircraft would be very useful for personal transport if you lived in Dubrovnik and had some money. The strip of Croatia north from there to the rest of Europe is unpopulated and well suited for building new airports.
The value of aircraft is the ability to go long distances. The lack of a Europe-wide Experimental category that allows IFR, long distance operations means that most innovative GA technology never gets to Europe, only the homegrown microlight stuff which is interesting and fun.... but also very expensive, not greatly suitable for export, and not greatly utilitarian.
The number of innovative light aircraft ideas that has come out of Europe is endless. For instance, few people remember today that Bölkow built production aircraft from wood, metal, and composites in the same Laupheim factory 40-60 years ago. They built a nice all composite 4-seat single, the first ever and still flying today, and it went nowhere. The whole thing collapsed, just like so many similar ventures. The issues are mainly political and to some degree cultural. The microlight movement seems to me a great response, although not greatly exportable due to the high aircraft costs.
PS My ELTs are 121.5 only and will stay that way.
The strip of Croatia north from there to the rest of Europe is unpopulated and well suited for building new airports.
Unfortunately we are not in the "building new airports" era, even the USA are in the "closing airports" era these days. Croatia has pretty good GA infrastructure although pricey. Greece generally lacks infrastructure and good politics. Indeed, Greece could be GA heaven. Every tiny German island has an airfield with a few Euro landing fee and fuel nearby, imagine Greece had that. I would probably be flying in Greece most of the time!
For instance, few people remember today that Bölkow built production aircraft from wood, metal, and composites in the same Laupheim factory 40-60 years ago. They built a nice all composite 4-seat single, the first ever and still flying today, and it went nowhere. The whole thing collapsed, just like so many similar ventures. The issues are mainly political and to some degree cultural.
To my knowledge, the only commercially successful new US aircraft design since the Bölkow failure is Cirrus. What else is there? Diamond although not that successful.
The lack of a Europe-wide Experimental category that allows IFR, long distance operations means that most innovative GA technology never gets to Europe,
Eventually we will probably see a pan-European regulation. Whether it will allow for IFR remains to be seen. I am not even sure it's a good idea.
only the homegrown microlight stuff which is interesting and fun.... but also very expensive, not greatly suitable for export
Companies like Flight Design (CTLS/CTSW), Remos, Pipistrel and Dynamic export the vast majority of their production.
Achimha, Van's Aircraft seems to be doing quite well commercially. The industry continues to evolve. Cirrus themselves have greatly contracted but experimental aircraft designs enjoy continued success. I have friends with their employees building aircraft components (composite CS props for 100-400 HP and landing gear/brakes) at a very good rate, with only a small fraction of their volume going to certified aircraft. The 'action' in US certified aircraft is rebuilding what's already out there in the field, or even scrapping them to free up the engines for experimentals. Lycoming has built over 300,000 piston aircraft engines, designed for very long life and multiple overhauls - how many more do we need?
Re microlights you forgot Tecnam :-) By export, I meant outside of the EU. Very few of any of the European microlights to be seen in the US in relation to the overall GA scene, their sales are presumably to smaller markets. To compete in the US market their price would need to be halved.
While I've still got your attention, do you think there will be future progress in opening up any of the barely used or closed Air Force airports in Germany to GA operations? For instance, Laupheim, Furstenfeldbruck, or (perhaps even further into the future) Erding? These are existing facilities that greatly outclass what's used for GA in Germany now. It seems a shame to me that they just sit.
While I've still got your attention, do you think there will be future progress in opening up any of the barely used Air Force airports in Germnay to GA operations? For instance, Laupheim, Furstenfeldbruck, or (perhaps even further into the future) Erding? These are existing facilities that greatly outclass what's used for GA in Germany now. It seems a shame to me that they just sit.
Laupheim is open to civilian users from what I know. Fürstenfeldbruck (Fürsty) is a very sad story. It was recently closed after years of fights between the operator (Bundesland) and the users, many court rulings, etc. BMW wanted it for safety training and Bavaria always does what BMW wants. The locals were in favor of closing the noisy airport, now they have BMW customers on the racetrack from 08:00 to 20:00. They deserve no better. And keep in mind the BMW logo is a spinning propellor. This company killed GA in Munich. Erding is supposed to be closed in a few years, right now it is Luftwaffe only. Munich will be without GA airport and just this year the government officially removed the goal of having a GA airport from the development roadmap. Munich is a very sad story, the worst of all large towns in Germany when it comes to GA.
There are positive examples of military airports allowing civilian users or being converted to civilian airfields. The former US Air Force airfield Bayreuth was handed over to the aeroclub this year. Husum up in the north became civilian -- (with a fence in the middle of the 3000m runway because the German army still has a bomb storage there).
For Munich, what about EDMA?
My ELTs are 121.5 only and will stay that way.
The problem is that unless they know where to look, within not too many miles, they will never find out on just 121.5.
You may as well wear that Brietling ELT watch and get some street cred for the £2500 
The GA situation in Munich strikes me as emblematic given the potential utility of GA to local business and large amount of aircraft activity that was formerly in that area.
EDMA (Augsburg) and Landshut (EDML) appear to be the same driving distance from the center of Munich, on opposite sides of town. I guess it would depend what side of town is of interest. Either is roughly an hour away by road according to Google.
