Doctors are the most Lucky of all villagers
3 reasons
1.They get to rest when there is no work
2.They have to be scolded to do their work
3.They don't have to do anything when we're not playing
If you think about it, that mirrors real-life doctors quite accurately.
In RL, doctors can only do so much studying; they then have to learn from experience with real cases of sick people.
It's not really true that they don't do anything when we're not playing. Lots of times I've opened a game to discover a doctor has advanced to Master while the game is off. A glance at the log file will often show them looking for sick people to heal, and successfully healing them. In addition, young doctors generally advance to adept on their own by studying the strange plants whether the game in on or off, as mentioned in other posts above.