The best solution is a nationwide license and ID, issued under the executive authority of the president. It would be visibly different from any other, perhaps with a racing stripe on it.
In big letters, in Mexican (whether the person speaks it or not) would be the statement,"Issued under the executive powers of the president, this ID card is valid for driving anywhere on US territory, and for all banking and voting purposes."
In fine print on the back, in English, would be further information. "This card is given under the assumption that the holder is an illegal alien, does NOT have any auto or liability insurance, is illiterate in ANY spoken language, and is exempt from any test of driving skill. Alcohol and/or drug levels allowed in the blood are 100% higher than state laws that apply to everyone else."
To further streamline the process, and save money, there would be one generic license with a man's picture, and one with a woman's. The generic equivalent of Juan and Mary Jane doe would be used for everyone. No place for a signature, and no bar codes, magnetic strips, or RFID chips. Let's see Gov Moonbeam try to beat that.