AAC is not free and you have to pay licensing. Answer to all your questions is simple- money
Apple and MS (MS is part of the licensing group, so probably pays way less) paid a lot of money to have it included into OS. You can use it in other apps, like Resolve does.
Linux is not MS or Apple and have no such a money or need to include AAC decoder and pay huge licensing fees.
Ffmepg route also won't work (as you described). You would need to obtain libraries yourself and then Resolve could link into it, but this is also grey area and BM simply doesn't want to do it to upset industry partners or face some legal actions.
Whole licensing crap is complex and even uses of free ffmpeg libraries in paid software has rules and limitations. Resolve already uses "ffmpeg" code. If it was 'easy' then AAC decoder would be in Resolve years ago.