I doubt that AI will lead to a post-scarcity society. It depends of what you mean by "post-scarcity". The amount of good and services will always be finite regardless of how they are produced.

> and the corporations and governments that control them rapidly have millions of useless mouths to feed?

I always struggle to understand this. Maybe I'm missing something. Who's buying what AIs produce if nobody has an income? You can imagine a scenario where corporations only trade between them (so only shareholder benefit from the production). However in such a scenario who prevents other people from spawning their AI systems?

I also doubt shareholders can actually consume all the GDP by their own. If production is so high that they can't and other people are poorer, then prices must come down. This combined with the fact that you can use your AI to produce services, makes me skeptical of these claims.