This was the Framers’ intention (in today’s terms) when they made natural born citizenship a requirement for the presidency. Dual citizenship did not exist when the Constitution was written. The Founders wanted the Commander-in-Chief to be 100% American with no citizenship of any other country at birth.
Even a relatively small fraction of the voters can enforce this requirement by just refusing to vote for an ineligible candidate under any circumstances. Presidential elections often turn on a few percent of the vote. Put loyalty to the Constitution above that of a self-interested Party and they will very quickly learn to stop running ineligible candidates.