Thus, from a wealth standpoint, a system with less unemployment is preferable to one with more.
Proponents of basic income usually claim that when people are freed from the drudgery of working a normal job, they will be free to be creative, to take risks, to start businesses, and that this new productivity will compensate for the loss of productivity in the traditional system.
But that's all that is: a claim. It's completely worthless without some kind of data backing it up. It's akin to a preacher saying that God exists because he said that God exists. It simply has no merit.
So would the loss of productivity be compensated for by the increase in physical and mental well-being? I have no clue, nor do you, nor does anyone, because we lack data.
So let's get the data.