If they are here and not being removed, they should have to pass any test that a citizen must pass in order to drive. There should be a special category of license which solely indicates that the bearer is sufficiently competent to drive. In-person appearance should be required to apply, no mail service other than notices to appear.
Now for the sweet part: Illegals driving without it would be immediately deported. And all those who applied have admitted to their illegal status, making them easier to locate. Any misstatement on the application (address of residence in particular) would also result in immediate deportation, as would failure to notify of new address if moving and insurance status.
They should not be allowed to drive!!!!