You are ignoring the fact that illegals get jobs without IDs. The reason is pretty simple, because of unemployment and withholding taxes along with copious paperwork for deducting employee expenses from the business revenue, it is easier and cheaper to hire illegals for cash.
I am not ignoring that fact. However, employers argue against rules cracking down on their hiring of illegals by complaining that they can't tell if ID is false or not. OK, now the IDs will be of much higher quality. Which means this law can eventually be coupled to much stiffer penalties for hiring an illegal.
In the end, illegal immigration will be curbed by three actions - better border control, cutting off illegal access to government bennies and services, and cutting off the demand for illegal labor by making it too risky to hire illegals. Improving standards for driver's licenses and outlawing their issuance to illegals is a big step forward towards the second and third actions.