DH did loads.
He works a shift rota so it's maybe a bit different.
In the end it's about what works for families. I do think though that it seems women are often expected to do everything in our society- leading to women doing too much after cs, and I wouldn't be surprised if it contributed to pnd.
Being sleep deprived is grim.
Anyway he took 2 weeks pat leave 2 weeks hol so a month for each child. While off obv he did loads. I had a CS each time so that covered most of the 6 weeks you're supposed to take it easy. If you've got a toddler it's really hard not to do things you're not supposed to do.
I BF but he'd get up in the night bring me the baby. If they cried but not hungry he'd cuddle them down to sleep.
When DD1 was tiny she would scream from about 10pm to 4am and we took it on turns to stay with her downstairs so the other could sleep. While he was off obv.
I also had pnd with both and so he looked after me carefully.
In the end it's up to the family. I do know lots of men who 'work late' openly saying it's to avoid bathtime/ bedtime though.
I suppose in the end I think lots of men could probably do more. On other threads on here it seems like they just don't see it as their 'job'. And someone else will do it so that works fine for them iyswim.