In some states, that is only true if the person does not live in your household. I’ve lived places where people residing in the same household were not covered unless specifically listed on the policy.
We have USAA and our rates didn’t increase when the guys had learner’s permits. As soon as S2 got his license (second semester freshman year of college) we had to affirmatively add him to the policy. He was 500 miles from home and was rated as an occasional driver. He lives at home now but doesn’t have his own car. He has had no incidents, so the premium is pretty low. If he gets his own vehicle, we will take him off of our policy.
S1 had a permit but only did the classroom hours – did not actually drive. He’s almost 26 and still doesn’t drive (I feel he should have that life skill, but he has decided that he gets around just fine with public transit, work shuttle, his bike and Uber/Lyft). USAA called a couple times while he was in college to see if he had gotten his license.
I would never exclude a family member from an auto policy. The liability exposure if something were to happen…terrifying. You may be able to get cheaper auto insurance rates if you have an umbrella policy that covers excess liability beyond what’s required by your state for your auto coverage. This also saves us $$.
The type of car your S drives also makes a difference in premiums. Agree with others to shop around.