The short answer is no, it's not a good idea if you can secure a seat in other universities which specialize in your domain. Here’s why:

• IITs and the NITs are institutions for Engineering and Technology solely. Humanities in these institutions are mainly supporting departments.
• Only due to the presence of guides, they do offer Ph.D. in humanities anyhow.

Considering your field, IIMs, TISS, and other apex institutions in Humanities or management studies make the best choices for you.

Go for Ph.D. in IITs or NITs only if you could not get admission into the top humanities and management institutes. Opting for research in an institute that doesn’t specialize in that domain is not a wise choice. However, you can consider top IITs like IITD, IITB, IITM, and other old ones as they carry a lot of exposure with them.