In the future, do bathrooms need to be cleaned? If yes, is it cheaper for that to be done by a person or by a robot?

Obviously, it is in the interest of the robot manufacturers to make the robot just a tiny bit cheaper than the person, so you'll buy the robot and the company makes the maximum amount of profit.

Now, if society breaks down and there's no one to consider buying the robot—well, that's not good for anybody, which is why I suspect society will find some way of working this out even if it's not ideal. But whatever, I don't particularly want to argue this point.

What I do want to argue is that there probably isn't a universe in which all white collar work goes away but blue collar work is still around.