Correlation does not equate to causation. Kohli got lucky that he is leading a well oiled indian cricketing machine, seeds of which have been sowed by Ganguly, Dravid, Dhoni and the big BCCI money pumped into every facet of the game. Kohli's captaincy in of itself is quite ordinary and tactically poor. Captain increases or reduces the performance of the team +-4-5% at best and if the gap between two teams is 10-20% and both play to par, in most games captaincy will not make any difference.
You can take credit from any successful captain in history with this train of thought, because no captain can win matches with mediocre players or turn hopeless talents into world beaters. No captain has a magic wand.
However, Kohli has also played his part in turning India into the must successful Asian Test side of all time.
Dhoni had all the money, resources, and the momentum created by Ganguly, and yet when he retired from Tests, India was ranked 5th in the world with a poor, lethargic fast bowling attack.
The difference between Dhoni and Kohli as Test captains is visible when you look at the performance of bowlers like Ishant Sharma and Umesh Yadav.
Both were completely different bowlers with negative body language. Kohli took them under his wing and they are now different bowlers. Ishant Sharma in particular went from being the butt of jokes to one of the leading Test pacers in the world over the last 5 years.
His dramatic improvement in performance under Kohli is not a coincidence. It is what inspiring leadership does.
Kohli is a great leader. His intensity and competitiveness has rubbed onto his players as well. He has made the pace bowling attack a vital cog of his team instead of simply using them to rest spinners in-between spells, which is what Dhoni did most of the time.
Our fans (not talking about you, it is a general point) need a coping mechanism. They expected India to get crashed 4-0 after the Adelaide Test and Kohli leaving and all the injuries that took place, but the quality and fight that this Indian showed over the last 3 Tests is something that they have a hard time accepting.
So now the coping mechanism is that Kohli is a poor leader, had he stayed India would have been whitewashed etc. etc.
Our fans always need something to cling on.