This is a theory I can't support well beyond hypothesising about what a post-employment democracy might look like, but I strongly suspect democracy doesn't work in a world where voters neither hold any significant collective might and are not producing any significant wealth.
Democracies work because people collectively have power, in previous centuries that was partly collective physical might, but in recent years it's more the economic power people collectively hold.
In a world in which a handful of companies are generating all of the wealth incentives change and we should therefore question why a government would care about the unemployed masses over the interests of the companies providing all of the wealth?
For example, what if the AI companies say, "don't tax us 95% of our profits, tax us 10% or we'll switch off all of our services for a few months and let everyone starve – also, if you do this we'll make you all wealthy beyond you're wildest dreams".
What does a government in this situation actually do?
Perhaps we'd hope that the government would be outraged and take ownership of the AI companies which threatened to strike against the government, but then you really just shift the problem... Once the government is generating the vast majority of wealth in the society, why would they continue to care about your vote?
You kind of create a new "oil curse", but instead of oil profits being the reason the government doesn't care about you, now it's the wealth generated by AI.
At the moment, while it doesn't always seem this way, ultimately if a government does something stupid companies will stop investing in that nation, people will lose their jobs, the economy will begin to enter recession, and the government will probably have to pivot.
But when private investment, job loses and economic consequences are no longer a constraining factor, governments can probably just do what they like without having to worry much about the consequences...
I mean, I might be wrong, but it's something I don't hear people talking enough about when they talk about the plausibility of a post-employment UBI economy. I suspect it almost guarantees corruption and authoritarianism.