It wouldnt make sense fir Tsunade to waste time training a chuunin or junin to become a medical ninja, because they already specialize in fight and right now it would be a waste of recources to take any of the capable fighters away from missions. Sakura is the perfect candidate to become a medical ninja because: 1. great chakra control 2. great ability to learn (maybe it is just because she is a bookworm, but so what that is kind of one of the main themes of Naruto, that if you work hard enough you can accomplish anything) 3. she has displayed a great level headedness in combat and an ability to see through enemy plans and techniques, and eventhough there have been several occasions where she is completely clueless, medical training would enhance her previously evident ability to respond to a situation with the technique necessary e.g. dispelling the sleep illusion in the chuunin exams. 4. the only the sakura really lacks at this point compared to her teamates is amount of chakra and a reprotoir of powerful techniques, Tsunade's training would help her with both of these.

I wouldnt expect Tsunade to train Sakura nonstop i think one of the biggest reasons Tsunade is willing to take Sakura on is that Sakura has the will and drive to achieve without Tsunade leading her the whole way. I imagine it will be much like Naruto's Resengan training, where Jaraiya would introduce a concept but then leave Naruto to figure it out on his own (for the most part anyway).