Because of Sakura not coming from clan that possess KKG or Doujutsu, the only choice for her is to learn something that not involved KKG or Doujutsu.
And she had a capability to be a good chakra controller and also good learner.
As for Tsunade she also not possessing any Dounjutsu or KKG but inherited Senju body power. And she and Sakura is actually on the same boat. And from there we can get the idea why Sakura is the most suitable to be Tsunade's Student.
If we take Hinata or Neji. they came from Doujutsu using clan. And most of Hyuga abilities is connected to their eyes power. And Tsunade doesnt have Byakugan to teach her Hyuuga student more effectively. In the end all Hyuga potential become wasteful because they're not using Byakugan base techniques much, just CES.
Get Hyuuga to train another Hyuuga because Tsunade couldnt developed their potential very well. Same as other KKG base clans.