Sacking Kohli is not the solution, appointing strong selectors seems right solution to me. If BCCI wants to solve this situation for good (although according to them its not a big issue, or there is virtually no problem in the current system) then everyone/majority of em need to be strong enough to stand against the bullying which Virat does sometimes.
Don't think that it is going to happen anytime soon. Virat Kohli has grown bigger than the team. Even MS Dhoni, at his peak never enjoyed this much dominance. The BCCI could think about taking disciplinary action against Dhoni (in case it was required), but doing so against Kohli is unthinkable. Now Kohli has become so powerful that he give orders to the coach and the coach follows them (rather than the other way around). And also, as long as the team is doing well no one really cares about the other aspects (which includes selection).