How would voter ID laws prevent non-U.S citizens from voting?

[gergroy]

richardhutnik said:

Kasz216 said:
Require a social security number to vote or an ID form that requires a social security number/green card number.

The system looks like it is full of holes now.  Because of this, I was asking how, under current conditions, is adding a voter ID requirement going to address the issue?

how would not requiring an official ID be any better?