>>Just something as simple as encouraging the adoption of language Y at home, and encouraging (not necessarily forcing) its use in schools, the media, etc. should do the job.

You seriously think people are simply going to throw away their linguistic culture, literature and other major accomplishments which are happening from at least some 3000 years old(Nearly every South Indian language will fall in this bracket) and then adopt one common standard which is not even spoken by 10% Indians? All for what?

Compared to any South Indian language, Hindi is a baby. And even that is saying something.