I'm pretty sure you have to be pure of heart to pull the Master Sword. Why are the stones necessary then? To connect the Master Sword of OOT to the Master Sword LTTP, and to give you something to do in the first half of the game.

I have a reasonable theory that the scattering of the stones in OOT may be part of a compromise between Hyrule and the surrounding tribes, to keep Hyrule from hogging the triforce. The evidence for this is unfortunately largely circumstantial. The windows in the back of the room spoil that, but in politics a display of compromise can be as valuable as a real one.