I don't know the best way to implement it, but I think it is necessary if you want to prevent wealth inequality from getting worse, faster over time.
What you are proposing is a good thing (greater efficiency) with a negative side effect (tilting economies towards the rich) but rather than tax the bad thing, you're taxing the good thing in order to reduce its negative side effect.
For whatever reason it seems like taxing robots is more socially acceptable than taxing the wealthy.
But these two often overlap. If any actual revolutionising automation by robots is coming, only the wealthiest corporations/people can and will afford it. As your parent poster said, robot tax is just trying to make sure that they won't hold on to their money under the mattress until the end of time. Redistribution of wealth is critically important.
The second is the idea that the owners are less likely to circulate money in the economy than the employees. There’s no value to the owner in sitting on that money, so why would they?
Second, the point you're getting at is trickle down economics. Personally, I don't think it works.
If you took a single production line and replaced the workers with robots - then yes. Those workers have lost their jobs.
However if there was a second hypothetical production line that made a product that was now economically viable (or just cheaper) by partially automating it, then that's made more manual jobs available (maybe the line didn't exist before, or now as the product is cheaper, there can be two lines).
So you've still got people working - and you've now also got cheaper/new stuff for them to buy.
Watch making is a good example. Wherever you are on the planet, you can afford a watch - something that used to require incredible wealth. This is due to new tech and automation. Doesn't mean that nobody's handcrafting cogs with little files, just means that those watches are now only being bought by the wealthy.
Whether it'll work out for individuals though - well the system doesn't care (and that again is a defining concept)
What is different now?
And broad application of AI is nowhere near.