It seems to me that the issue here is inadequate care, not whether men should be on the ward all night or not.
If new mums had proper support and care in hospital, then they wouldn't need their partner there all the time.
35 years ago I had my twins in a large teaching hospital in Yorkshire.
I had been in for a month before on enforced bed rest, shared ward of about 8 beds, all mums in waiting. Normal traditional visiting hours only. It was very boring- lights out at 10 and the only tv was in a separate lounge.
After the twins arrived I was kept in for a week, all the new mums had a separate room, patient loos were down the corridor. This was normal practice- all first time mums were in for at least 4 or 5 days then. Partners could stay longer if mum was poorly, but I don't remember any staying overnight. Other visitors and partners of non poorly mums had to stick to the normal biding hours - 3-4 in the afternoon and 7-9 in the evening iirc. Sister would get quite fierce with anyone who outstayed their welcome.
We were taught how to bath our baby, the midwives helped establish breast feeding, we got lots of sleep. There were ward sisters, midwives, the ward cleaner, auxiliaries- the only complaint I had was the food. DH brought me regular food parcels from home.