[Theoria]

As it is, the electors would be the only people required to prove citizenship when voting[electoral college]. Electors decide who the president is. There is no right to vote for electors in our system, aka Bush v. Gore dec.

[Amendment10]

Not only does 12th Amendment prohibit state winner-take-all laws for electoral votes imo, but the Founding States never expressly constitutionally gave ordinary voters the power to vote for president like they did for representatives.

Also, Section 2 of the 14th Amendment indicates that only citizens can vote in federal elections.