Being stay at home parent is super lonely experience, basically the most lonely occupation you can have. In most jobs, you meet people and you do talk to people without trying to. Fairly often, they are unavoidable whether you want it or not. If you are at home with a kid, you are truly absolutely alone, unless you organize something. Every other guy here on HN complains about Covid being lonely, but it was less lonely and socially easier situation than being stay at home parent.
So, alternative framing is that women stopped organizing these as their need do organize them went down. And men did not had that need in the first place, so it did not changed from their point of view.
And simultaneously, it ceased to be acceptable to be the kind of dad who spends multiple evenings a week with buddies, not really spending time with his kids.