US insurance rules are set by states and they differ somewhat. There used to be a few states that did not require insurance but I don’t know if that is still true. Also if you have a car loan the bank or whoever gives the loan will require insurance.
I think it may along the lines of - if the daughter is not listed on the insurance policy and has an accident, then the insurance company will make good the damage but then chase her to re-reimburse them. It depends what insurance she has by herself and what it says about borrowed cars. A lot less hassle if the driver is listed on the insurance. And as pointed out, every state has its own peculiarities.