I don't think this is some false progressive promise at all. Work is freedom and independence. Through work people express themselves at a cognitive and creative level.

It's not just about 'snazzy careers'. It's about self-realization. When given the choice in countries with tons of generous child welfare policies like in much of Europe, women still defer pregnancy and prefer to get an education or a job, and I don't blame them because honestly most people grow tired of being a stay-at-home parent very quickly. It's just a menial, not really inspiring, and not very social job.

I know a lot of guys who said the same thing you said, that they'd love to stay at home. All who did now work again full-time, some even admitted directly to me how much they hated it after only a few months and how much they missed work.

I think this attempt to romanticize stay-at-home parenting is basically cultural nostalgia. It's also interesting that you frame it as a women's job as others have pointed out, because the only reason women had to do it in the past is because they didn't get much of a say in the matter.