I'm not advocating the replacement of workers with robots and I do not think the GP was either.
But why not? Clearly, if a robot can do hard labor instead of a human, that should be preferable on humanitarian grounds. If it can also do it for cheaper, then, as you rightly note, it should also be preferable on economic grounds. The only argument to the contrary is that people who are pushed out of jobs by robots (and this will clearly keep encroaching, so a laborer can only "retreat" by re-qualifying etc so far) are out of their source of income. But if the sole reason why we give them jobs is to provide them with income, then it's basically just a thinly veiled form of the broken window fallacy.
We may have to reign ourselves to the fact that if robots can replace unskilled workers, some people will need to be supported by the public somehow.
That was the point that I was trying to make. Automation is inevitably going to drive down the cost of labor so much that selling it to obtain basic income will cease to be a realistic proposition for a significant part (long term, probably the vast majority) of the population. At that point we'll need to come up with some other arrangement.
Note though that the long-term proposition is not "some people supported by the public". It's the reverse - "the public" supported by a few people (those who would still have jobs - like programming the robots). In fact, it's not even clear what "support" would mean, since, if most of society is basically on free welfare, then money is not really a universal medium of exchange anymore... the few people who still work - whom would they get the money for their work for, and what would they spend it on?
Hell, get that proportion high enough, and you'd probably have people competing to get a chance to do "real work" - for free.