People to people communication is necessary and movement anyway happens across the borders ... either legal or illegal !
Commies have already done tha in many states including Mumbai. Crores of Bangladeshis are already here.
Now when I say trains are necessary .. becoz we have to keep our contacts with our neighbours. India, being a bigger neighbour has the responsibility of keeping its relations in cordial ways.
India can not alone progress and get richer while Bangladesh, Nepal, Pak & SL will go bankrupt. Even though its not India's fault, adverse economics will have adverse effect on the nation-nation relations.
Its like having your bunglow (or a villa)in the middle of slums ...