In a lot of places, you need to ask permission before you're even allowed to build a hospital. I think that fact, and the process attached to it, helps keep the supply low.
Hospital complexes are large, distinctive, and attract a lot of traffic. Check your city’s zoning map - existing hospitals are probably in a zoning category of their own, and they’s unlikely to be any spare hospital-zoned land. At minimum it would take a big land use fight, before even getting into medical and public health regulation.