Hindi as a link language is a non-starter, unless people in North Indian states also learn South Indian languages.

To simply understand this point, forcing exclusive use of Hindi in Central government institutions gives an undue advantage to people from North India.

You mention in principle, but in practice the opposite happens. I am an East Indian who has spent all his life in South India I speak both Hindi and a South Indian language along with my native tongue. When North Indians come to South India, and stay for a long time a majority of them refuse to learn the local language whereas every South Indian who has spent time in the North picks up Hindi.