There’s a reason that hospital and hospitality are such related words. They were originally more like inns with physicians. You paid for a room and received treatment in it. Profit was certainly part of the picture.
There are many variations of the theme throughout history that may be called hospitals, but any large facility for housing the ill would have tended to have no private owner. Doctors visiting the homes of patients has been more common historically than patients visiting homes or offices of doctors.
One problem is that as technology has been advanced to treat health conditions, care for individuals has been forgotten in its basic essence of being humane and social.