What if men providing resources to their families is a drive that runs deeper than some kind of vestigial macho chauvinism? We already have mass depression, isolation, falling educational outcomes, suicide, and even radicalization of men who are unable to find purpose to attach themselves to in the modern economy.
Are we to gloss over the function and instincts of half the population as an attitude problem? Social engineering is way too easy inside a theoretical bubble, where expecting billions of people to fundamentally reconstruct their entire identities can be handwaved in two words. Progressivism is supposed to meet people’s social needs, not dictate them.
If it is true—and I do not for a second believe it is—that the latter is an actual biological drive in men specifically, then that's something we need to work on developing strategies to mitigate and work through in a healthy way, because it's not helpful in our modern society. Y'know, much like our panic response is not helpful in our modern society, and when someone has an overdeveloped one, we treat it as a mental illness to be treated, not a "function and instinct" that needs to be catered to.
Personally, I find the idea that men have a biological imperative to be the sole reason their families survive to be nothing more than a ludicrous extension of modern toxic masculinity, on par with "of course men will rape women, once they get aroused they can't help themselves, they have a biological imperative to propagate their genes."
Back to the claim, sexual dimorphism and sexual division of labor are such a fundamental and ubiquitous element of human physiology and society that it is a mistake to assume there is no adaptation to speak of, or that the role of the male provider is suddenly maladaptive.
It may be that we can restructure society by common agreement in a different way that continues to harness the productivity of testosterone. That is not what you are espousing. Your ideas are a form of social high modernism which assumes the sexes are interchangeable as a premise, then categorizes any deviation as toxic and unhealthy (or even on par with rape apology, which is just... you've got to be kidding).
I don't see any basis to believe this other than that it simplifies the theory and makes utopia seem within reach. But we do have evidence to believe that sexual division of labor is effective (in a word, "civilization") and we are also seeing festering male issues in the decades since we've been experimenting with the alternative premise.
In the current system, if you want to do X, you have to prove to the people who are willing to pay you a living wage/market rate to do X that you are worth hiring to do it.
Under a (hypothetical) post-scarcity system, if you want to do X, you find a group that's working on X and say you want to spend some of your time working on it, and you do it, possibly getting trained first if you don't yet have all the skills needed. Depending on the particular work and/or the particular system that's been implemented, either your financial needs are entirely taken care of by the UBI, or you get the UBI and then you may get paid some extra to do X—but the amount you would be paid to do it would be determined by completely different factors than under today's system.
This more-or-less eliminates the gap between what people want to do with their time and what society will let them do with it...though it will still require a cultural shift away from the idea of the Rugged Individualist Man Providing For His Otherwise Helpless Woman And Children With Nothing But The Sweat Of His Brow.