Good heavens, I was born in the early 60s and my dad did all that stuff. He used to cycle home as quick as he could after work to cook dinner and spend time with his children. He changed nappies, he bathed us: the only things he wouldn't do was sewing and mending because he'd never been taught and my mum had.
When my youngest was born I was quite ill and my parents stayed with us. Dh and my dad and my mum took it in turns to do the nappies after each feed. It was lovely to see that my 68yo dad hadn't lost his touch.
My late FIL was born in 1909 but was also a hands-on dad when his time came in the 60s: one of his favourite stories was how he was stopped by a police officer pushing a pram through London in the middle of the night and had to explain plaintively that "the little bugger won't sleep"- at which the officer nodded sympathetically, having clearly been there and done that. To FIL it was natural that his wife needed to sleep too, and if the only way of achieving that was by taking his son out, then that was his job. When he retired earlier than his wife, he took over the running of the household. This was a man who could remember visiting France before the First World War. Still perfectly capable of cooking dinners and looking after a family.
As for dh, he basically never sat down when I was still busy. (In fact, he is ironing now, so I should probably go and do something productive too)
He did nappies and anything else you can do with a baby from day one. When we realised my career prospects were going to get damaged by being a SAHM for too long he took a day's unpaid leave/week to be a SAHP so that I could up my qualifications. When I went to conferences he ran the household- which wasn't really that different to running it as a team when I was at home.