Sorry. Couldn't resist.
This is absolutely the most hairbrained logic imaginable. I think its actually a typo, and that they really meant to encourage illegal "immigrants" to obtain driver's licenses.
Legal immigrants have zero difficulty providing proof of their status: an immigrant visa is stamped right into their passports. And most legal immigrants of proper age do two things in their first weeks within the U.S.: they get a Social Security Number and they obtain either a driver's license or a learner's permit.
Whether illegal aliens do or do not have a driver's license is a complete red herring and a lame excuse for loosening the law. Illegal aliens are guilty of a misdemeanor by being here in the U.S., and then they are guilty again of a felony (in most states) for driving without a license. They shouldn't be on our streets at all.
The underlying problem is that states have no real ability to to assess citizenship or immigration status. We could of course ask the states to begin "profiling" applicants by asking anyone with an accent to produce a valid passport, but that might be a little much in this day and age. Common sense is not exactly in vogue in our federal and state bureaucracies.