What you consider basically perfect might be what already exists. You have to really go out of your way to find games that aren't compatible with for anything pre gamecube. If one emulator doesn't work with a game, chances are another will. Its just that getting genuinely perfect 100% compatibility out of one single emulator is a VERY tall task.

To use your example, one of the most popular GBA emulators is mGBA. While they don't list the exact percent, here's what they cite on their website:

How good is compatibility? mGBA emulates two platforms currently, with the work-in-progress medusa version supporting a third:

Game Boy Advance emulation is currently very good. There are known bugs and a small handful of games that don’t boot. Game Boy/Game Boy Color emulation is good. Most games work but there are still plenty of bugs. Please file a bug if you find a game that doesn’t boot. DS support is very early and only available in the medusa branch, which is not under active development at the moment. Current bugs can be found on GitHub for GBA, GB/C and DS