You'll want to take a look at the rental agreement. Chances are extremely good that it contains terms that look a lot like this (example from Avis for US rentals):
- Prohibited Use of the Car. Certain uses of the car and other actions you or a driver may take, or fail to take, will violate the
Rental Agreement. A VIOLATION OF THIS PARAGRAPH, WILL AUTOMATICALLY
TERMINATE YOUR RENTAL AND IS AN EXCLUSION TO AND VOIDS ALL LIABILITY
PROTECTION AND ANY OPTIONAL SERVICES THAT YOU HAVE ACCEPTED, INCLUDING
BUT NOT LIMITED TO SUPPLEMENTAL LIABILITY INSURANCE, PERSONAL ACCIDENT
INSURANCE, PERSONAL EFFECTS INSURANCE, ANY ROADSIDE ASSISTANCE PLAN,
EMERGENCY SICKNESS PROTECTION AND LOSS DAMAGE WAIVER (LDW) OR PARTIAL
DAMAGE WAIVER. IT ALSO MAKES YOU LIABLE TO US FOR ALL PENALTIES,
FINES, FORFEITURES, LIENS AND RECOVERY AND STORAGE COSTS, INCLUDING
ALL RELATED ATTORNEYS' FEES, LEGAL EXPENSES, FEES AND COSTS THAT WE
MAY INCUR. It is a violation of this Paragraph if any of the following
A. You use or permit the car to be used: 1) by anyone other than an
authorized driver, as defined in paragraph 5;
In short, if you allow an unauthorized driver to drive the rental car, your rental agreement will be automatically terminated, along with any insurance coverage involved in the rental.
What does that mean? Well you're now driving a car without a valid rental agreement. If you get caught out (likely if you're involved in an accident, though it's not impossible for it to come up in the course of a police stop), that could potentially mean you're violating state law by driving a car you have no right to use, which could get you banned from the rental car company if not in more serious legal trouble.
And there will likely be significant issues if you are involved in a collision. Does the unauthorized driver have auto insurance? (Even if your credit card insurance does cover the claim, most credit cards that offer rental car coverage only cover damage or theft of the rental car itself, not personal liability for injuries and property damage outside of the car.) Does their personal insurance cover them when they're driving a car they're explicitly not authorized to be driving? Probably not; standard insurance policy forms have an exclusion for this:
Loss to any "non-owned auto" when used by you or any "family member" without a reasonable belief that you or that "family member" are entitled to do so
In short, letting an unauthorized driver operate the rental car voids your rental agreement and risks leaving the driver uninsured. Neither of those are good situations to be in.
Some rental car companies will waive the additional driver fee for members of AAA, Costco, or USAA, and they may not require a fee for the primary renter's spouse or business associates (as part of a corporate rental); check the specific rules of your rental company for details.