My DDs are both in their early 30s one married with DCs and the other lives with DP no DCs. The younger, married, one is a SAHM. Her DH is very hands on with the DCs and does quite a bit of the cooking. Housework, not so much, but she's at home all day and he isn't, so not unreasonable.
I was actually having a conversation about this a few days ago with the older one. She and her DP both work full time, both doing more than one job with very committed hobbies. If housework needs doing it's done by whoever sees it needs doing, whatever it is, and they both do the food shoping and cook.
But it seems that with most of her friends - who all work - and work mates this isn't the case, their DP/DH don't expect to do housework.
They live in a very 'hip' sort of town that most people would assume is full of 'new men', unfortunately, when it comes to pulling their weight in the home and with childcare these 'new men' seem to have retained a great many of the 'old' attitudes and see these things as 'women's work'.
My mother was a SAHM and my father worked full time. However he was very hands on with the DCs and would do a lot round the home. He was born in well over a century ago. It was just the way he was.
I think a great many people will leave stuff to someone else if they can get away with it and unfortunately there are still a great many men who are happy to go on doing that. I don't believe that most women today won't 'put up with it'. I suspect that for a great many women nothing has changed.
My exh did absolutely nothing around the home or with the DCs. I never found a way to change that. His attitudes towards me is the reason he's my exh. There's only so much pushing you can do if someone won't budge.