This is kinda naive. Even robots are not free to produce or maintain. Literally all of the labor works would be replaced, but I don't see how or why would big companies/investors/rich people offer welfare to all the population that was living on labor works. A situation where a robotic economy would be achieved through capitalism advancement but abandoned afterwards would need a pretty big paradigm shift, or something akin to a worldwide (industrial or not) revolution.
Also, it could lead to a stagnation in all research, expansion and such. It's pretty easy to realize that capitalism won't cut it, but we'll need a new system that works.
What is known as "the economy" is really just one aspect of the human condition. Just because everyone would have everything they ever would want or need because all the labor is automated doesn't mean people stop competing with each other (because they literally can't.) It just means focus is shifted. Our statuses would just be decided by something other than material wealth.
Of course, people will never be 100% equal in terms of material possessions, due simply to thinking differently, or not caring, or what have you, but lets make an example of this. A very common thing humans have. Oxygen. There's enough to go around for everyone. No one cares how much or little oxygen you have and no wars are fought over it. If quite literally ALL labor were to be automated, our sense of achievement and social status would merely shift to something that was not common. Certainly there would be war, disease, and suffering, but the quality of life would be higher, and our "economy" would merely be based on something else like number of children, or whatever rare materials still existed. Animals owned, etc. etc.
EDIT: Also, to go back and address your first point. Sure, actual perfection is impossible--but it's our ability to imagine hypothetically perfect systems that allow us to advance our understanding. Also, IF there were unlimited goods/necessities/luxuries, why would people not give them out for free? They would have no value. Thus it wouldn't be offering welfare at all.