I agree that it should, but it may have helped to ensure that by setting some minimum requirements as to general knowledge and abilities, fiscal and monetary prudence, sobriety and honesty to qualify as a candidate.
To have a well educated and well informed electorate is a MUST for a true democracy to function, otherwise it is too easy to manipulate the result of any election.
Changing the Constitution to suite today's reality would help. To have Delegates and Electors travelling for days to convey the will of the people in individual States is no longer necessary. The Electoral Collage system is unnecessary in today's reality, when the result of popular voting is known nationwide as they are announced in individual States.
Doing away with this relic from a time long past would ensure that nobody can get elected President without receiving the majority of popular votes. Makes every vote count equally.
Black money is obviously the biggest problem, but also the easiest to legislate away, since it is NOT a Constitutional right, or obligation. Easy to say, impossible to do, unless the will of the people is behind such a change.