Who is the gatekeeper? I've read that either the GOP or Cruz certified each and every candidate as qualified, to the various state election boards. The NH heard and rejected a challenge to Cruz's eligibility.
So, for purposes of ballot access, the gatekeeper is the election board.
The constitution anticipates that the public could elect an unqualified candidate, and provides for actions to take in case the president elect is not qualified.
That's the way the system works in principle.
In practice, the system will capitulate to public belief. I agree with you, the fuss and furor is moot, except insofar as it affects individual voter's action in the voting booth.
Well put.