No. Hell no.
I fell dangerously ill 2 days post section. Extreme fever, tachycardia and I stopped breathing. My 4 bed bay had to be cleared out. Imagine that with other sleeping bodies? It just isn't practical nor is it safe. Maternity wards have emergencies just like any other ward.
The nurse rounds at 6am would wake everyone up. The quiet moments in the morning before the ward opened to visitors when a Dr could do his rounds (yes, I know more often than not this happens during visiting hours too), women could shower with relative privacy, babies were safe to be left for 10 minutes, OT comes to see post section mums. how would that work? Wards have the visitor timings for a reason. Its only going to make life harder for every one to change them and lets be realistic. Mums are, on average, only in hospital for around 3 days post birth. 24 hours if they are lucky and have a straightforward delivery. Surely all partners (male and female) can see the benefits to letting new mums have privacy and breathing space from the real world for a few hours!
Then you have to remember the maternity ward should be a safe space for all women at their most vulnerable. There will be women on those wards who will have been abused, victims of domestic violence and raped. Those women know they have the right to ask for a chaperone with male doctors. What about with other men during the night? at least with visiting hours they know its only going to be for so long. They can have a family member or friend with them during that time but at night? ugh!
single women. Just another slap in the face for them when they have no one. Just no... I was a single mum. Gave birth alone. midwives were fabulous but if I knew I had to go on a ward where fathers could stay overnight I would have discharged myself. I wouldn't have felt comfortable.