Illegal aliens are only relevant to a discussion of voter ID laws if those aliens have successfully registered to vote. Preventing illegal aliens from registering to vote is just as effective as requiring ID on election day, but doesn't have as many negative side effects.

Plus, exploiting a lack of voter ID requirements by impersonating a registered voter on election day has pretty much the worst risk vs reward balance of any form of election fraud. It's hard to identify large numbers of registered voters who are unlikely to actually vote, it's hard to gather enough individuals to impersonate them, and it's pretty easy for any large-scale effort like this to be exposed.