The Star Trek ideal is that everyone contributes to society not because they get an instant-gratification reward of wads of cash, but because humanity has evolved to the point where individuals strive to better humanity rather than line their own pockets.
And as mentioned, that ideal was brought about by the replicator. If you can make anything you want out of thin air, money is useless.
Things got confused in the lore, btw, because Kirk mentions selling his house in Generations, but DS9 had several scenes where Jake and Nog argue over the fact that humanity has abandoned money. Voyager also mentions Fort Knox having been converted to a museum after humans abandoned money.
The robots we're discussing are going to be our replicators.
Sure, they can't make scarce materials, but they can go get them whereever they are, for free. Found oil somewhere that currently isn't exploited because it's too expensive to extract? Robot labor is free. Go get it.
Find raw materials for making solar panels on Mars? (assuming we ever run out of. . Sand) A robot-crewed spacecraft is on the way.
In short, once robots are making everything for us, we might as well have replicators. Hell we probably WILL have replicators by the time we manage to run out of something - after all, with robots doing all our work for us we can concentrate on higher pursuits. Even the most prolific inventor today still has to take time to mow the lawn, cook dinner, and pay bills.
BTW, you might want to give DS9 another shot. I hated it too, but decided to give it a second chance and am watching it on Netflix streaming. It's actually pretty good, and is much more nuanced and complex than any of the other ST shows.