One of my LEO friend said the conservative estimate is 98% of the illegals have no drivers license, and a similar number have no insurance. This has been the norm for longer than I care to remember. But as gypsyman said, this has been going on for years, not only with the illegals, but with American citizens too.
Many states have laws that are designed to prevent this, but they don't work. Here in Texas one must show proof of insurance to obtain a license plate for the vehicle. My wife has been an insurance agent for many years, she says "they come in and apply for insurance, the agency writes a binder good for thirty days and sends them a bill for the premium. The individual takes the binder to the Tax Assessor-Collector, gets his license plate, and never pays for the insurance which is canceled after thirty days. There are no provisions for the insurance company to notify the state that the person does not have insurance, (sometimes they may transfer to another company, but rarely) so that person continues to drive with out any coverage.
Approximately 25 years ago I lived in a curve on a very busy road. During the period we lived there, we had six vehicles totaled in three different accident. In one my twenty-one foot Skeeter Bass Boat was also totaled, , and in another over ten thousand dollars in damage was done to my home after one of my vehicles was knocked through the wall. In this accident, the guy was not only drunk, he was driving a stolen car, was an illegal immigrant, and a convicted felon who had been deported, yet returned to the states. He was not charged with driving the vehicle, or causing the accident because no one could place him behind the wheel, yet he was the only one there after the accident, bloody, and stumbling around trying to get out of the vehicle when my son and I went out to see what was going on after hearing the crash.
While I agree, a lot of the apes on the road with no license, or insurance, are American, I think today the majority are illegal.