As an aside I feel really strongly about this OP that it should never happen. My hospital doesn't allow it and frankly I thought the visiting hours for partners(9am-9pm) was way too long.
Fathers are not patients, they are technically visitors and all this "bonding" guff is nonsense - do you really think if you don't stay with your baby 24 hours a day for the first 4 days you've forever missed the "bonding" window of opportunity?
Not to mention it takes care and attention away from women who don't have the support, who don't have someone to fetch them things and fight their corners, because one thing I have learned working in healthcare is that visitors are disruptive as hell even if they're there to 'help' their loved one. You would have coped if you think you needed your DH because you would have to - other women do every day, the single mothers and the ones in hospitals that don't allow men overnight, it wouldn't have been pleasant but you would have coped
This whole "he's the parent too" - so what. When it comes to giving birth and having a baby so fresh and new you're still in hospital, men and women are not on an equal footing. The feelings, privacy and safety of women come before that of men, even the nice ones
It all feeds back into the inequalities in healthcare that women face. We are mere vessels when we give birth, our feelings don't matter, men should be considered before us. I don't care how nice your Nigel is, 4 more bodies in a ward full of vulnerable women and babies is harmful to the patients there and don't get me started on the behaviour of many men (yes yes NAMALT but a significant number ARE LT for it to be a problem).