This is kind of a stretch. The article also mentions “manner” which is an option against “place”.
They’re better ways to argue against mail-in voting, like citizenship verification.
Take a look at the clause again.
The Times, Places and Manner of holding Elections for Senators and Representatives, shall be prescribed in each State by the Legislature thereof.
Notice the "and". That has meaning. It means that each one of the items listed "shall be prescribed". That means that "Places" must be prescribed. The items listed are not just an "option". All three (Times, Places and Manner) must be prescribed. The state legislature cannot skip prescribing "Places" just because the "Manner" is prescribed.