Depends on people.
Would AIR 1 like to join IITP?
I don’t think so.
Would AIR 10K like to join IITP?
They would want to but they won’t get to.
Should you join IITP?
Yes, absolutely. If that’s the best option available to you, don’t let stereotypes and hearsay stuff misguide you. It’s a fine institute and if you got a chance to be there then, by all means, take it.