“What is the problem to add a small air driven (by a prop) alternator to the wing or the aircraft's belly?”
I have a friend with a vintage machine who has this arrangement. The generator has made quite a difference to performance (85 hp 2 seater). He has it feeding direct or charging a battery when free. He can run his radio on it no problem, but the Transponder (with separate encoder) takes all the output and flattens the battery in about 2 hours. I do not have details of the generator, but Francis (from the LAA) was of the opinion it would not be suitable for most non electric LAA types.
Rod1