The main accusation against Kohli is that he does not take any tactical decisions if things are not going your way, the team wins because of his aggressive approach and the way in which he leads the team from the front scoring runs and on their day they will defeat any team in the world and the upcoming world cup will be a big test for Kohli as a captain in T20 internationals.
The 2021 T20 World Cup will be conducted in India and that should give a huge advantage to Kohli & Co. But if India's performance is less than satisfactory in that tournament, then I expect the BCCI to take some tough decisions, including making Rohit Sharma the captain for the shorter format. Aggression on the field needs to be backed up with performance. If Kohli is not capable of that, then someone else needs to be given the responsibility.