A UBI would be nice, but it wouldn't make gender specialization less useful.
Second Wave feminism is essentially White men sending their women to work so that Black men wouldn't get those nice new jobs and move into their neighborhoods and maybe, God forbid, marry their daughters. It was Tom Sawyer selling his pals on the joys of whitewashing the fence. For all but a statistically insignificant elite, work is punishment for original sin, the point being not that God ordained it, but that the Bible recognizes how unpleasant it is. Why would anyone aspire to it? (About forty years ago, when a lot of women were entering the professions, I heard one woman lawyer ask her male law partner's wife what she was "working on." "My backhand," she replied. Diff'rent strokes or diff'rent folks.)
Anyone who knows anything about economics knows that competition is never a choice; one competes, or one observes a custom under which there is no competition. One cannot oppose the custom and expect not to have to compete.
It takes a village, but only non-commercial women can build and maintain a village. Of course it's work. But to say it is unpaid work is to say that it produces no benefit for the worker, and that's not true, even if we ignore the contingent fee wives get through community property and other laws of marital economics. Nothing is perfect, and every system is going to have its genuine horror stories. But the best is the enemy of the good, and gender specialization has a lot of good going for it.