I qualified in IIT in 1972 without coaching; This may or may not conclude, that it is not required.
I personally feel that coaching only gives practise and mental training & preparation to handle the exam ...
Like if I had taken the coaching, I would have got higher rank (AIR:All India Rank) of say wthin first hundred (100) instead of 1206; Similarly for CAT, it gives practise, time management startegy and mental preparation etc. It gets u to know and get the first hand experience of doing it from the experienced ...
So it goes without saying that coaching does not make a dull student into a brighter one ... the innate understanding, interest, brilliance & brightness must be there so that it can be sharpened!