In my opinion, Rohit should be allowed to captain the T-20 team while Kohli should be allowed to captain the ODI and test teams. This is the optimal solution.
Treating Kohli who has achieved so much for his country in this manner is seriously messed up. Won't be surprised if he gets replaced by Rohit as the test captain sometime in the near future.
Every team follow mainly 2 setup
-1 captain for limited overs _White ball and 1 captain for Red ball
-1 captain across all format.
In such case BCCI has a every right to ask Kohli to step down from the ODI captaincy as Kohli voluntary decided to step down from the T-20 captaincy, in their point of view having 2 different captain for white ball cricket doesn't make sense. You can make case that Virat has done so much for the Indian cricket and BCCI should treat their legend with respect, which is 100% true. I think this is where BCCI fails royally as the organization on countless occasion.
Virat is strong figure in Indian sports but he's nothing when comparing to BCCI, actually no player comes close. Just look at old cases of Kapil, Sachin (not good example but still valid), Gangully etc when they were playing for the India. You can't arm twist powerful board for long, also we shouldn't forget the recent Kumble(Kohli) controversy over his coaching gig. Kumble had to resign because Kohli wanted him out. Kumble also made contribution to Indian cricket and he's also legendary figure in the Indian cricket.
BCCI clearly didn't handle this situation nicely but Virat is professional cricketer, he should be mature enough to see the writing on the wall and accept it grace fully similar to Sachin. Sachin also failed to delivered as a captain so he gave up the captaincy and played under 4 different captain after that. If Virat had one ICC trophy under his belt then his case could have been very strong but unfortunately he has none despite performing well in Bilateral series. As far as Test captaincy goes, he's good for another 2-3 years and its not going to change because no one comes close to him but power structure in white ball cricket has changed, for good or bad, well time will tell.