the coach in the context of the Indian team is nothing more than a showpiece.
Take the context
The selectors pick a team that is suites to their interests
You burden the team with a bunch of depleted old guys and some of the captains favorites who are exhuasted and have little to contribute (sachin tendulkar and Harbajan singh are examples)
Others in the team are concerned about the endorsements and on making the most of their dwindling careers. What do they do - Try save their their skin with a one off performance that serves the team no good rather - Case in point Ganguly and Sehvag
Predictably the team gets the results it deserved
Whats Chappel got to do with this mess, If the coach needs to take ownership so do the selectors. Would they be prepared to step down if Chappel is removed... Naaaaaaah I dont think so
The best option would be to persist with Chappel and give him a free reign, that would bring in the results