You're basically talking about the democratization of capital. Companies and their owners will resist it tooth and nail, since they want to reap the dividends.
I don't think we'll get to a world like that, with former laborers owning the automation that replaced them, without some kind of radically new regulatory regime or an outright revolution.
Only to the degree that they've been trained to see themselves as temporarily embarrassed millionaires, and identify more with the interests of the owners than their own personal interests.
I don't think "most voters" who don't see themselves as temporarily embarrassed millionaires would shed a tear if CEOs, business owners, members of the management and ownership class, etc. had their ability to own robots limited. At least after some consideration of what where most labor was replaced by automation would look like. So I object to the idea that such a law would be "a non-starter for most voters."
I'm not a legislator who's spent a lot of time thinking how such a law would be implemented, but you could probably accomplish with some kind of per-capita ownership limit. A CEO could still own robots, but not any more than a pleb to make a difference. They'd have to employ the pleb's robots instead of buying all they need themselves. That gets around the problem of classifying people. There's still the problem of determining the overall number to be rationed, and that probably requires a bit more thought than I have time to give right now. Though part of it could probably be modeled after the present-day labor market.
And why not take your idea further. Only one person per truck? Per acre of farmland? Per airplane? Per computer? Per pencil? Per lathe?
Why shed a tear over lost crappy factory jobs when those people might be better employed fixing the robots, at a higher wage and skill set?
Full automation essentially means that labor is no longer necessary - the owner of the capital can have it produce wealth directly (and robots can fix robots, after all - although the system breaks down long before that, since even when you have humans fixing robots, one human can fix a lot of robots - so you're still employing only a minuscule part of the labor pool). From a perspective that is concerned solely with economic efficiency, all those humans are now simply redundant - they can go and starve to death for all anybody cares. And from a perspective that is concerned purely with property rights, theirs is the freedom to do so, since any other course of action - say, expropriating some robots that would then feed them - would be in violation of those rights.
Somehow, I don't think they will care for it, though. If you make enough people desperate, you get torches and pitchforks. And judging by how revolutions went historically, those torches and pitchforks won't be directed against the capitalist class first and foremost - they'll be directed against those immediately accessible that still have cushy jobs and the associated lifestyle, i.e. whatever remains of the high middle class by then. And if we don't want that to happen to us, we've got to start working out practical solutions, and using our political power to force them through.
We obviously have a problem, but it's how to make the poorer more valuable through education and training, not how to make the well off less valuable through arbitrary productivity restrictions.
IE, sorry, doctors make too much money so we've capped their patients at 20. Versus, doctors make too much money, so we've streamlined more people to become nurse practitioners and PA's.
I'm not sure this is true, and the only way I can see it possibly be is because "middle class" is a very fuzzy category that's defined relatively to others, so it can grow in absolute terms by e.g. lowering that relative standard. Income inequality has steadily grown, not shrunk. Concentration of capital at the top, and concentration of income from that capital, has also grown.
> not how to make the well off less valuable through arbitrary productivity restrictions.
You're looking at it the wrong way. It's not about restrictions on productivity. It is about redistribution of capital, and prevention of it getting concentrated too much in one hands at the point where labor is going to lose access to more and more of it to feed themselves via wages. I don't even thing that capping ownership of capital is the right way to do so. Taxing the hell out of it would be a better idea.
And education and training is not going to do anything to the fundamental problem of 100 people competing for 50 jobs.
Those workers should feel free to do that right now and spend their money investing in capital.