No, we don't need caste-based reservations in the private sector. (And I'm saying this as someone that's ST). That would further increase the divide between castes, and I've never heard of anyone being denied a job in private sector based on their caste. It's definitely not the norm.

Reservation should be meant to uplift 1-2 generations, I don't see the point in giving reservation beyond that. I've seen so many rich people from lower castes getting into institutions easily and also availing scholarships by faking their parents yearly income. The whole system is rigged to be honest.