Although I don't think coaches play a very big role in individual matches or series..I think Fletcher was a bad choice for India....
A coach's role is to groom players..develop their already existing skills..manage their work load, training, fitness.. I don't think you can blame Fletcher the last 1 year though..lot of factors like work load and poor fitness levels of senior players are beyond his control.
Bangladesh have just won a series against an established side and they don't even have a proper full time coach but the development of players like Tamim, Shakib, Rahim, Mahmudullah..you have to attribute that to Jamie Siddons..
So on that point, I don't think Fletcher has a lot to give to the Pujaras, Kohlis, and Sharmas in India which they already don't have.