I had my son at a public hospital that only had single rooms (bathroom was ensuite, shared with the joining room). They were more than happy for husbands to stay over too. It was an excellent place to birth and stay at.
I had 2 nights there before my son was born (induction - gel first night and next morning, waters broken in afternoon and wasn't until the next day that syntocin was used as contractions didn't kick in enough to do much). It was hard to sleep with hearing babies in nearby rooms crying and women making birthing noises.
After my son arrived, I didn't notice those noises so much, as I was too busy sleeping.
Unfortunately can't birth my twins at that hospital, so bit more pot luck whether I get a single or shared room. Apparently the hospital I'll be at has a priority for single rooms for c-sections, multiples and sick mums. They also bend the rules to allow husbands/partners to stay over if you have multiples (apparently they stopped doing this as a general rule, due to too many aggressive partners causing problems with staff, sad).