Considering the size of the wizarding population in Britain, it makes sense that there's only one wizard hospital. I imagine if there were other hospitals, they wouldn't be as busy. But at the same time, safety is an issue, as if something happened to St. Mungo's- an attack or a highly contagious plague, etc. it would be pretty vulnerable. I also wonder how wizards get the injured to St. Mungo's so quickly. It would make sense to maybe have some small clinics throughout the country that were magically connected so a patient could get emergency treatment if needed and then transferred over to the main branch for recovery. These clinics could also be utilized in the case that St. Mungo's is compromised.

Chelsea/Ravenclaw