The result sheet clearly reads against Fletcher. It's not a new appointment- he's been in charge for three whole years, so that's three years of mediocrity for the Indian Test team.
Let's not blame the players for everything going wrong- in the Dhoni era, player losses have been mounting. Each time a player is lost (dropped), the replacement has not been good enough. Quality in selections has also been compromised, as top Ranji performers are being ignored to favour Club Dhoni, some State teams with powerful lobbies as well as a misconception that only the youngest players are good enough for India.
Ravi Shastri's not really been given a fair try here. He's in as a coach. He's supposed to run the team from the bench, plan things out for them, and keep his best men in form, laying out what's best for them. He's not had that one great Ashes triumph and two Asia series wins like Fletcher, but he'll be better fit for India because he understands the system better. Foreign coaches were needed to bring in modern methods, which have soaked into the dressing-room atmosphere. Moreover, plenty of Indians are doing coaching programmes and have been certified, and a few have had experience either with States or Associate Nations. Let's not rule them out totally.
What India needs, as coach and captain, is someone who's more practical, and can plan and study the scene (and the opponents) before the event, and try a few things out of the box, and even take some bold measures- fair, not questionable ones like the earpiece orders, but at least something like Ian Chappell making his pace bowlers field in slips.