I do believe that nobody "belongs in the kitchen" as far as gender roles go. What we're up against is the weakness of the family unit in society and the breakdown of lasting friendships contributing to mental health issues. Online social lives are objectively bad for us, and I'd argue that the dopamine hit is just helping burn our dopamine receptors even more.
Regardless this reminds me of the classic argument that was had back in the 80's about the kitchen itself, that it's more "efficient" for people not to cook at home but to go to a place that prepares food en masse for a community. This was during the Soviet Communism era and there was a side debate going on. Western culture favored the family unit, while a communist concept favored social efficiency at the cost of liberties.
I don't think it's regressive to desire to have more time to be with your kids, whether it's day care, school, etc. The real issue isn't economics and progressive concepts, I think we'd all agree that a robust public education system is valuable, and that we should have economics that let us pick our kids up from school rather than send them to a day care. It's not about sending anyone to the kitchen.
I like our kitchen, I like cooking food for the family, and I even enjoy it as a way to wind down after work. Modern life not supportive of tight knit communities and lasting relationships is complete bullshit. Modern life in that viewpoint is the continuous hustle culture and prioritization of work over a fulfilling life experience, and in my opinion your viewpoint is regressive for that reason alone. Kill hustle culture, eat the rich, and let's have economics that give us a choice.