Nope partners shouldn't be allowed to stay.
I type this from a gynaecology ward where I have been for the past week. At night and weekend it is extremely understaffed (3 staff to around 20 patients). A majority of the patients have undergone extensive surgery that includes the removal of additional organs, not just womb/ovaries.
A number of these women are also receiving various cancer treatments on top of their surgeries. One woman also has broken bones.
A number of these women could do with the support from their partner not just in terms of physical care, but also emotional support and some are, in private rooms as should be the case in postnatal wards.
Wards are noisy places to begin with without the disruption of additional people staying, hence the NHS are trying to put strategies in place to stop noise pollution which accounts for a high rate of patients discharging themselves early and jeopardising their health.
What is needed is more staff on wards, not partners. I stayed for over a week for each of my 4 births and I never witnessed the struggles that these women are going through at the moment.
If a woman wants partners to stay they either pay for private room or have a home birth, but inflicting more noise at the detriment of everyone else isn't on. This daft policy also sends home 2 tired parents when dad/mum should be well rested to take their partner and child home and there he can look after them.
Thankfully this hospital came to its senses. They tried it, concerns were raised including the extra strain having 'helpful' partners had on staff and the policy was scrapped. In its place, as it should be, maternity wards are properly staffed.