This is what layoffs have been about since the pandemic. People in fear of losing their jobs do extra unpaid work and aren't asking for raises. The theoretical potential of AI gives companies the excuse to fire more people. The investment itself is directly used as a reason of why they need to cut back on labor.
Any sufficiently sized business can only feed the insatiable hunger for ever-increasing profits ultimately by cutting costs and raising prices. And what do we have now? High inflation and a decline in real wages. CEOs are just following this playbook.
And the result is that society is bouldering towards collapse. We're seeing the first hints of this with the youth unemployment crisis [1][2][3].
Also, who is going to buy anything when nobody has any money?
[1]: https://www.americanprogress.org/article/americas-10-million...
[2]: https://www.brookings.edu/articles/twelve-ways-to-fix-the-yo...
This assumes that a mass consumer economy is necessary, when it isn't. Mass consumption is relatively new, for most of history economies functioned with just a small consuming elite and large underclass that consumed very little. We are already approaching that again in the states given that the top 10% of earners are already responsible for nearly half of all consumer spending.
There's a floor even in a mostly automated economy where some services are resistant to automation simply because the human element is the product. Luxury hospitality, personal care, etc. That billionaire is going to want a human masseuse, not a robot.
A highly automated economy could stabilize like this with a small elite population consuming luxury goods & services, served by a low-wage economic underclass human workforce.
Its certainly not a pleasant society, but its also not unsustainable given enough oppression or pacification (bread and circuses anyone?)
As for services increasingly unaffordable by the workers providing them, that's Baumol's cost disease (https://en.wikipedia.org/wiki/Baumol_effect)
I don't have any sources regarding someone preferring humans for certain services over robots, just intuition there, and the fact that consuming human labor and time is itself a status signal of wealth, and the current growth of personal services.
As for connecting the dots, look at Brazil, one of the world's most unequal economies having a small consuming elite and a much, much larger low-wage service underclass. The gulf states as well. Granted, their circumstances don't map cleanly to a post-automation Western economy, but it does demonstrate that a largely bifurcated consumption based economy can exist and can be mildly stable.
Whether the US falls into that direction too will depending on politics. A bunch of mid-career knowledge workers aren't going to willingly to flip burgers in a service economy without some serious surveillance and oppression. But when thinking about it in those terms, the recent push for mass surveillance laws and tech along with the increasingly dangerous rhetoric around protests and "domestic terrorism" start to make sense.