Dude I cleared both JEE (Mains) and NEET, n still decided to study in a T1 NLU (w/o quota in case u r wondering). Though I may be the only guy who has done it but still for info.
Bro you are so wrong if you think NLS Nalsar kids are JEE rejects. Engineering rejects turning to law might be true for lower end law colleges but not for Tier 1 law schools. It was my dream to be in NLS and I made it true by sheer hard work in class 12th. It is true that for jee rejects the last bastion is a generic management or law degree from lower end colleges. That is to do with how easily both are achievable.
Law is equally a respectable profession.
Though I may be the only guy who has done it but still for info.