I'm not sure if this is sarcasm, but I will assume that it's not and I will bite anyway: because the President necessary put the good of the US States over everything else, including his own family (if necessary), "unquestionable loyalty to the US", basically.
That requirement is pretty much impossible to clear if you wasn't born in the US (and hence your relatives isn't US citizen). So for all practical purposes, you might as well codify it.
For private sector job, however, there seems to be no difference in motivation between a citizen and a non citizen in working for the organization (we're there to make some $$$ and keep on with our lives). So yes, I'd love to see the damn requirement get removed :-).