Are you agreeing that the Constitution itself draws a distinction between (mere) citizen and "natural born citizen"? It sounds like it. (Which is good, since it is the text of the Constitution already.)
I do think there should, at a minimum, be legislation that defines responsibility for ensuring any candidate meets all the eligibility criteria and defining each of the eligibility standards. We could do that more permanently by amendment, but I have no problem with doing it initially by legislation.
A son or a daughter born in London England to an US Air Force Airman or Officer and his wife is an nbC. This individual may run for President after 14 years of Residency in the US. The son of the French ambassador born in INOVA of Fairfax (VA) hospital is not.