People shouldn't just worry about "no insurance" but also underinsurance. Minimal insurance in many areas is ridiculously too low. If you're signing up to do this as a driver you better #1 Tell your auto insurance company and #2 Up your insurance levels to the max (something you should probably do anyways if you can afford it).
If you're signing up to do this as a rider, well I don't think you should given the insurance problems and you not having any guarantee that someone will be held liable if they cause an accident.
Getting into a bad accident with an underinsured driver at fault is a life changing event.