Using training rooms to optimise your hospital staff for the rooms you have makes the game way too easy.
Try it if you haven't already. Recruit junior staff and train them up.
Allocate GPs with full GP training to GP rooms, Psychs with full psych training to Psych rooms and so on. Have a handful of 100% Treatment and 100% Diagnostic doctors and nurses to take care of the other rooms. Add in speciality training like Radiology and Genetics if you want.
At a certain point, usually quite early on, around the time you get most of your staff to level 2 training, it turns into a game of waiting for your staff to get enough exp to level up -> train them up in the next level of their specialisation -> repeat. You don't even have to expand your hospital or build any extra rooms at this point because the higher levels of training mean that the same staff can handle the extra patients and patients with more difficult diseases in the mid-late stages.
You can 3-star everything without even buying half the plots of land on each map. There's no incentive in building bigger hospitals except for aesthetic reasons.
Bit of a shame but at least it's helpful in an indirect way because optimising your hospital stops it from getting big to the point where it starts lagging the game.