We simply cannot judge a player’s competency following just one test series. And besides, even as a fan, regardless of how Indian players play in the 5-test match series vs England, win or lose, it was always quite expected that they will lose. Defeating the English, in test matches, on their home turf, is difficult—at least at this moment, given just how decorated their team looks. There’s Joe Root as captain, Alastair Cook, Jos Butler, Sam Curran and Moeen Ali. Can’t recall when was the last time the England team looked so balanced and impactful.
So, to reiterate again, Indian test team was expected to give a tough battle to England in the 5-test match series; however never was it to win it. Right now, after 3 matches, the table is 2-1 in favor of England. 4th Test match is underway. If India is to win the series, they have to win the ongoing and the next match. If England wants to win, all it has to do is make draws.
Now talking about your question in specific, should Virat Kohli be removed as Test captain if the team loses this series. The sweet answer is NO! Indeed, if you overlook his performance as captain in the third test, the series hasn’t been very flattering to his real recognition. In the early 2 matches, things didn’t exactly click for him. However, even then, Kohli stands as one of the most successful Indian test team captains.
In fact, only recently, Kohli took over the test records of Sourav Ganguly as captain. He has led the team in 38 tests till now and has lost only 7 matches. Ganguly has 21 victories in his books from 49 matches in which he had led the team. Of course, MS Dhoni still stands as the MOST successful test team captain, leading the team to 27 victories out of 60 matches. I believe that it’s only a matter of time Kohli takes over Mahi. And as Mahi’s fan, it would be sad for me… :(
Over and all, Kohli is amazing as test captain, and except for a couple of players in the team (Ajinkya Rahane and KL Rahul), I don’t think anyone even has that X-factor to take over the captaincy role from Kohli. So, even if India loses the 5-test match series vs England, the magic of Kohli will remain just intact. He should (and would) lead the Indian test team till the day he decides to retire.