For better or worse there will definitely be services that AIs will use to get bodies (human or otherwise), for a fee. This already exists, just not in the mainstream.
At the risk of sounding dystopian: in a world where humans don't have jobs, what's your price to have meaningful work larping as an AI's flesh? Would it be any worse than any other job? There's some terrible employers out there and they're not AIs.
There's another interesting subtler take on this, "Maneki Neko" by Bruce Sterling, where this system drives society but less explicitly.