" single purpose hospitals would be a bad idea - what if you're delivering a baby and the mother starts bleeding profusely?"

you would clearly need to provide immediate care, but then move them on as soon as possible to a general purpose hospital.

Here in NZ we already do something like that specifically for birth - mothers have the choice of using a midwife and having a home birth, and the midwives move the mothers on to the hospital only if problems present.