Dumping one provision of the Constitution because someone deems it irrelevant in the modern age opens wide the door to dumping other provisions of the Constitution because someone thinks they are irrelevant in the modern age.
I get that. I wouldn’t dump anything. For the “natural born citizen” requirement, I believe a Constitutional amendment to change it — or at least clarify it — is in order.
I’d also suggest that changing provisions of the Constitution related to procedural and governing matters is far less benign than changing provisions of the Constitution that reflect inalienable rights.