Beautiful, but certainly naive.
In order to access to those positions you need support.
This is how things usually work:
->X wants to become a president, so X enlists to a political party.
->After a certain number of years in such party, X has acquired enough support to become head of the party and it promotes his candidature for the presidency.
->X becomes president. (provided he chose the right party...)
Needed years to acquire enough support are usually less if X comes from a family with great influence or has strong support from a powerful lobby, the people or any other interested party, which usually also takes time. And obviously this person would have needed to work in order to eat, so even more time yet.
So why are Presidents usually old?
->Because he got in the party 20-30 years ago and needed that time to gather enough support. -> Typical politician/Pope...
->Because he got in the party 1-5 years ago and needed the rest of the time to become a successful businessman/actor/whatever (so he has support from certain lobbies). -> Trump/Schwarzenegger...
If the President was to be the fittest for the job (physical prowess or qualifications wise) he would have reached his position by mean of public examination. It could also be argued that the fittest for the job is the one with the greatest support obviously.
My 2 cents.