Long answer - On average, about 2000 students enter the IITs every year for their BTech (the number is higher if you include MTechs). To suggest that India produces just 2000 exceptional brains may not be correct. As with most exams, the JEE could very well be more of an elimination exam rather than an admission exam. Also, the plan to upgrade the RECs to IIT level is not really increasing the supply of top-level engineering seats. It is merely a re-christening of the RECs. I am not aware of the entry procedures into the RECs but by adopting the JEE, the RECs would be raising their standard a notch or two.
Also, instead of having a cut-off number of students as in the present case, it may be better to have an absolute measure such as, say, minimum score of 70% in each of the subjects in the JEE. The rationale being - how much better is the 2000th student from the 2100th. Instead, if an absolute cut-off like 70% (or any number deemed appropriate) is used, one will know for sure how a candidate measures up.