I live in Liverpool, a moderately large city in England (and work in the city centre). An hour's cycling, let alone driving, will get you basically out of the city. And, for all that there isn't space for vast exurb-style tract houses, there are a ton of houses of different sizes up to large detached houses with decent gardens, large parks, and all the other nice things.

Travel-to-work areas are circular-ish, and the available space for housing increases with the square of the distance. Accommodating a large hospital's workforce won't make a sizable dent in that. Compulsory tiny rabbit hutches in the sky it is not.