The IIT's do have a parallel-The Ecole d'Mines in France. The history, numbers, status and impact of both are equitable.
Speaking from experience of attending a course, interacting with IIT types both researchers and students and professor's-nay, bureaucrats; it may be time to fully capitalise on the IIT investment by 100% privatisation. Same with IIM's. Why?
IIT's are sitting on premium land. Considering they are totally residential instiutes, same as IIM's, where is the sense in said institutes retaining prime tax-payer funded real estate? Further, 21st century internet, distance and privatised lab enabled atmosphere enabled better dissemination of knowledge (lectures+labs) in a wide area spread with limitless enrollment. The funds for ramping up are locked up in the land w/o the original rationale.
This is unlikely because nobody wants to 'dilute' IIT/IIM eliticism. I have noticed IIT/IIM types to 'Shut the door behind them' to retain exclusivity, at the cost of the public exchequer. Imagine if similar amounts of public money's, goodwill and land were invested in Birla Institute of Technology or the Tata equivalent (not sure if it's Indian Institute of Science or TIFR).