As people seem to need to be entertained by real people, professional entertainers and athletes could survive.
But how could all the unemployed people afford to watch them?
AI might also need human receptionists if its owner needs human clients.
As long as AI is never allowed to develop to the point where it serves itself. However, it would only take one rogue software engineer to sabotage that.
I think that AI could be the doom of capitalism. For people to be sure of employment even when they are not really needed, some form of socialism might be necessary. It might even be necessary if people are going to live lives of leisure while AI robots do all the work.
When I was young, pundits predicted that technology would lead to society having more leisure time. As it turned out, that was only true in the sense that technology caused some people to become redundant and live off social security while others continued to work full time. Capitalists don't like to support people who are of no use to them.
Soon, Microsoft's innovations will give us AI powered by quantum computers. Any computable problem will be solved instantly by the equivalent of an infinite number of computers working together in an infinite number of universes. The most complicated codes currently used could instantly be cracked by brute force algorithms. (One way or another, China will, ahem, obtain the technology and develop it more cheaply, more efficiently and probably more quickly than Microsoft can. Perhaps if we all have AI translators, though, we won't all have to learn Chinese.)
If humans want to have a reason to exist, they will have to act quickly. Then again, if humans have to deliberately limit AI in order to have a reason to exist, does it still count as a reason to exist?
Who cares. I still want to exist, even if I am of no earthly or heavenly use.
I can think of another profession that many people might think is carried on better by humans. I find it interesting to contemplate that the world's oldest profession might also be its last profession.