The real issue is lack of staffing and incredibly poor and often inhumane care..
This is what MN should be campaigning about because women wouldn't need their partners with them if post-natal care was not so awful.
My experience with DS 2 mirrors a lot of women's experiences on this thread. I'd had an instrumental delivery (in pretty much the worst hospital in the country) so they insisted that I had to stay overnight. Apparently this was so DS could be seen by a paed in the morning. This, I was told, was Absolutely Essential.
So they packed me off to the postnatal ward, where they put me in a room at the furthest end of the ward from anything and everything, including the room where they 'served' food. They were supposed to give me painkillers, but I never got them. I dread to think what would have happened if the drugs I'd been prescribed were more vital than painkillers, especially as asking for them did nothing.
Because I was exhausted, in pain and struggling with DS2 I couldn't go and serve myself some food, or get a drink, so I had nothing to eat or drink until DH was allowed in for visiting hours (many, many hours later and a long, long time since I'd eaten due to a 36 hour labour). I got no sleep that night either because the ward was noisy.
DS never got to see a paed and by 6pm I was really fed up and desperate to go home. Eventually the midwife in charge of breast feeding support came round to help me and I broke down in tears, so she arranged for them to let me go home. DS saw the GP the next morning, a full 24 hours later than if they'd let me go home when I wanted to. It's not like either of us were under any meaningful medical supervision in there (in fact, the support provided by the community midwives was orders of magnitude better than what the post-natal ward could provide).
In that situation, having my DH stay with me would have made things much, much better for me because he'd have nagged about painkillers and fetched me food, etc. But that would only be a way of compensating for the thoroughly inadequate care I (and everyone else) received on that ward. So the thing that needs to change is the standard of care on post-natal wards so that women don't feel alone and abandoned and terrified as they struggle, exhausted and in pain, with their tiny new babies.