First, Southies are NOT immigrants in India - their ancestors have ruled the land that can be to some extent associated with present day linguistic states. For example, TN associated with places where the Tamil kingdoms, Chola, Chera, Pandyan, Pallavas ruled.
Second, southies, if they move up north, they have picked up the language of that region and they expect the same from the northies when they move down south.
Third, India is NOT like France or Germany or Britain - its more like the European Union. - that is also why it is called the Indian union. What you are saying is like asking the French to speak English in France for the sake of numbers of english.
Fourth, northies do tend to "force" their language or hindi on southies and also on fellow northies wherever they go or some are like you - trying to act as if they are doing a favour by NOT forcing their language on others - which aint a favour by any means.
Fifth, even now, the govt spends around 100 crores a year for hindi evangelization and the rest of the languages combined together get less than 10 crores for their development - which is lopsided and biased to say the least.
Even in 1965, when the literacy rate was a paltry 24 % and when we were importing 2 shiploads of wheat/day to barely survive the govt spent 2.1 Million US dollars for hindi propagation. This was the time when shashtri gave the famous call for fellow Indians to skip one meal a day since we were short on food supplies - this is the best possible example of "forceful imposition / usurping common resources for the benefit of a single language"
To spread Hindi, the government is spending $2,100,000 this year. - this is in 1965 !!!