It probably should be required for any government position where the holder of the office is expected to exercise their own individual discretion. The Federal government won’t grant a security clearance to individuals that owe substantial amounts of money, especially to foreigners, or who have deep personal ties to foreigners or ownership stakes in foreign businesses. I for one would like to know whether candidates would be eligible for a security clearance (though of course the President themself is not subject to most rules about classified information).
Perhaps, but though the Constitution lists only minimal requirements for the presidency it's clear that the authors had the belief that the will of the people should be curtailed in plenty of circumstances.
