Aye, there's the rub.
Can you name any federal statute that provides a penalty if a non-citizen votes?
The many related statutes focus on who can vote. Some provide penalties for making a false claim regarding citizenship but there is little by way of verification of such claims.
Of course, voter registration is the point of intercepting non-citizens, not after an election; however, there is nothing similar to a passport that local registrars can rely on for verification, so many make no attempt at all.
Most of our voting laws were written before inter state and international transportation became so easy and fast.
We didn’t have a lot of people moving around from state to state, or foreigners sneaking into the country by the train load.
The voting laws need to be changed to reflect the new realities of modern transportation.