The most likely scenario is that everyone but those who own AI starves, and the ones who remain around are allowed to exist because powerful psychopaths still desire literal slaves to lord over, someone to have sex with and to someone to hurt/hunt/etc.
I like your optimism, though.
When people starve and have no means to revolt against their massively overpowered AI/robot overlords, then I'd expect people to go back to sustenance farming (after a massive reduction in population numbers).
A while later, the world is living in a dichotomy of people living off the land and some high tech spots of fully autonomous and self-maintaining robots that do useless work for bored people. Knowing people and especially the rich, I don't believe in Culture-like utopia, unfortunately, sad as it may be.