Two forms of democracy are common worldwide:
- A parliamentary democracy where citizens elect a parliament and the parliament elects the executive (presidents, prime ministers, etc.).
- A presidential democracy where citizens separately elect a parliament and the leader of the executive.
There are good reasons from history and political theory to prefer one or the other. It weakens the separation of powers to have the executive elected by the legislative. On the other hand, the budget authority of the legislative controls key actions of the executive, so it would be inconsistent to have an executive of a different political orientation execute it.
But as long as India has a prime minister who is the head of government, it would be inconsistent to have a directly elected president who is head of state. If the ceremonial representative of the state has a popular mandate and the governing representative of the state does not, that undercuts the ability of the prime minister to govern.
So if the president was directly elected, one would have to do away with the prime minister position and adopt a system like the US or France (where the prime minister is appointed by the president).