many women perceive unknown males as less comfortable or safe to be around, and are more embarrassed, anxious and uncomfortable than they would be around unknown females.
I'm not blaming the entire male race for this, I'm sorry you feel it's mean to men, but this is the truth and the reason why mixed sex spaces are unfair. There are reasons why females don't feel safe or secure in vulnerable situations around unknown males, this is a fact, and if that's hurtful to males or to females who feel the need to stand up for males then they frankly need to give their heads a wobble.
Yes, I know women don't like it, I wouldn't like it either.
That doesn't mean it's "centering men" though, or acquiescing to their demands that is the motivation. It means a mixes sex space with unrelated people/strangers is a problem, when you typically have both parents wanting to be together with their newborn.
I think the issue about lack of care is a bit of a red herring, it's a problem, but not one that admitting men was designed to solve. Men began to be admitted to childbirth, and then the period after childbirth, because couples wanted it and it came to be seen as the best model for family centred care. There were plenty of doctors and nurses who didn't want it, and men for that matter, my impression has always been that it was more demanded by women.
It doesn't work well though with traditional wards. And I think we can also ask other reasonable questions about these problems. Nursing staff have a lot less authority over behaviour and guuests than they used to, and you get some pretty bad behaviour from both male and female visitors. Obviously some patients will not be easy ones, but even there, I think many people have a sense of entitlement to use services while acting like asses.
Also, what we should expect in state health service, is what we want always what we should expect? When this system was first designed it was very much a matter of people were very happy to have access to a hospital, for free, that had pretty good standards of care. Maybe you had a bed on a ward with a lot of other patients but that was far better than no care at all. People were pretty proud of nationalised health services in most countries they began with. But costs have skyrocketed in so any was as more has become possible, standards increased.
Those are in some ways unanswerable questions, but to me they can't easily be separated from a question like, can we build family rooms for people having babies in hospital, if we really think that is the best model of care.