It's fair to say that JEE has strayed too far from what most of us would agree should be its real mandate: standardization across the large number of Class XII boards. If it is not a standardizing exam, then what is it?
I want to consider the possibility that the JEE is actually a contest. That would make JEE rank (or, a seat at an IIT) a prize -- it's prestigious, it's highly coveted, it's scarce.
JEE, in other words, is a process very much like that used for selecting people to to represent India in the math, physics, or chemistry Olympiads. Only the numbers are different -- Indian Olympiads probably select a few tens, while the JEE selects a few thousands.
[JEE certainly has features that resemble the Olympiads: tough questions that require you to think creatively, questions that go beyond Class XII (even though the syllabus is nominally the same), questions that test your agility, time pressure, the need for intense preparation, etc.]
If this premise is accepted, then it is better to organize JEE like the national sports championships are organized, or like the Olympiads are organized. Lots of local events, which escalate to higher levels -- district, state and national level championships (and rankings).
This has the desirable property of selecting those who are 'good', 'motivated', 'hard working', 'persistent'.
It has the even more desirable property of eliminating a large number of people along the way, and fairly early in the process. We are talking about more than 90 or 95 percent of the students, who really have no business taking the JEE, who end up taking it because they think -- or their parents think -- the Prize is worth their blood, sweat and adolescent years.
People will say that there will still be coaching. Yes, there will be; but it will not be the dysfunctional, monomaniacal, it's-okay-to-neglect-school kind.
It will be small, sharp and focused. And it will help the right sort of people (willing victims, if you will!) : those who really have a flair for science, and enjoy doing intellectually challenging work.
If IITs want JEE to be a Prize exam, they are better off treating it as such, and take the necessary steps -- organize it like the Olympiads. Have multiple elimination rounds.