Good arguments. I'm just saying that the defense for the age limit would be the idea of 'reasonable' restrictions. As proposed for schools or churches.
Note, that I'm dead set against those except for highly technical reasons. However, the reasonable restriction mantra carries some weight with folks - as in the school debate where so-called gun rights supporters come out against school carry rights and babble whining scenarios of fear.
As far as medical exams for cognitive competency - I suggest they be instituted for the Congress and Presidency.