While I agree with you that it'll be nice if the villagers continued to study the plants, it is not necessary to keep a village running. I have several mature villages, andMaster Doctors in many of them.

Just like you need to train new villagers to be a parent when the older ones turn elderly or die, new doctors need to be "started." I'll either pick kids to do all the healing when I have an health issue, ir find one who likes "medicine." When the game is turned off, or switched to another game slot, those villagers will increase their skills and will often start healing villagers on their own.