There is a difference between “required” and voluntary action. Voluntarily producing one’s birth certificate may begin a tradition, but it does not make for a requirement.
***The required action is to qualify for the elibility of the office in this case, as set forth in the constitution. Of course, a constitutionalist would know that, and defend it as proper.
The Constitution doesn't require a presidential candidate produce a birth certificate for public approval - read it, the requirement just isn't there. Further, I don't recall any presidential candidate ever being required to prove his citizenship (McCain volunteered his and Obama did too, just not the long version), and I'm OLD.
The Constitution does require the president to be a natural born citizen, however it doesn't not suggest nor require any action on the part of the candidate to prove his or her status.