Unopened hospital does not compensate staff!
Bit of a fun one. Before clicking the "open hospital" button, your doctors are not salaried. Meaning, you have plenty of time to put them through training and to do research for free.
CS Edit: Link to the screenshots showing the problem.
I have news from the team - What you described is an intended feature. Our developers decided to leave it out in the game as it is not something game-breaking and takes a lot of time in-game to achieve. So enjoy these boosts!
Best,
Dominik