One problem is that AA/AAA primary cells are 1.55V or so when fresh, but there is no AA or AAA rechargeable replacement which is anywhere near this.
Standard old NICD/NIMH chemistry produces 1.2V and many/most products treat that as a flat battery, so you tend to get a very short life out of it… if it works at all.
The best that exists are the Sanyo (now Panasonic) Eneloop batteries which are nearer to 1.4V and these work much better. We use them at home everywhere. They also have a massive advantage over traditional NICD/NIMH cells in that they have a very low self discharge. Normal NICD/NIMH self discharge in a month or two, especially when they get old.
A properly designed product will either have a selector switch for primary/rechargeable and this alters the battery status determination, or will run down to say 0.8V. But almost nobody does this nowadays. And for primary cells it will give you a very late indication of a low battery; basically only just before it dies.
I use 2300mAh Energizer rechargeables and find them good. Haven’t noticed any dropoff in lifetime vs standard AA.
Using Duracell AA batteries I get a warning a couple of hours before they die.
I use NiMH rechargeables in my Bose A20; they certainly last many hours. Off-brand worked well with Bluetooth off; it did show “low battery” for a long time, but worked well.
I switched to Eneloop when I started using Bluetooth. It works well. Again, the A20 shows low batteries constantly, but that state lasts for many hours.
I start seeing on the “market” Lithium batteries in AA/AAA package format that provide 1.5V. Apparently some do that with a chemistry that provides more voltage, but they convert the voltage with electronics inside the package; others (non-rechargeable only?) use Li-FeS2 which provides a nominal voltage of 1.5V directly, good cold-temperature performance, etc.
The “disadvantage” of the “converted to 1.5V through electronics” is that they will hold exactly 1.5V until (nearly) empty, then will brutally drop voltage very fast. So your device will show “full battery” for a long time, and give very little warning of the battery emptying. While alkaline & NiMH give a more gradual slope of voltage vs remaining capacity.
