While there is clear division of class in India, the Prime Minister should choose to show humility to each and every person who is a citizen of his nation. Rather than allowing class issues to grow each generation, having important figured such as the Prime Minister show respect to all citizens would encourage the people of India to see each and every person in their nation as a respectable and valuable human being.
In this day and age it is odd to think of citizens bowing to a hierarchy. In some countries this is the norm but to view someone as a lesser person is not a good thing. We are all people and should not have to bow to anyone to show our allegiance. The symbolism of this is great though.
The Prime Minister absolutely has the right to show humility to others. Some people take this as a sign of weakness, but most would take it as a sign of strength. The Prime Minister is the leader of the people and to show that in this way is a huge plus in my book.
I do not believe that the Prime Minister of India is duty-bound or obliged to bow to the feet of a "lesser" person. The caste system in India is outdated however in order for the Prime Minister to retain his authority then certain levels of decorum and propriety need to be upheld.