Loco that argument doesn't fly.
Law enforcement has to FIRST suspect you are breaking the law AND THEN, if the required reasonable suspiscion is met that the individual suspected of a crime is in the country illegally, the cops can inquire into that individuals status. So, if the person stopped speaks english, has a valid photo id or some other form of identification that would tend to demonstrate they are here legally, the inquiry stops dead in it's tracks. There would be no reason to suspect that the person questioned by police (suspected of breaking the law) is in the country illegally.
The cops can only push further for an individuals status ONLY if they are given reason to believe (if they already suspect that individual is breaking the law). AND THE REASON CANT BE BECAUSE THE INDIVIDUAL SUSPECTED OF BREAKING THE LAW IS MEXICAN.
There is no need for national ID cards, or any of this other nonsense. It's a common sense law being used to combat a common sense problem. Don't commit any crimes, don't enter the country illegally, and if you are stopped by police don't show them phony documents and answer their questions dishonestly. Problem solved forever.