Legal Question in Personal Injury in California

It would depend on your level of maturity. If you have sufficient insurance and sufficient driving skills, your driving should not be a problem. It does appear to be a bit over protective, unless you have shown yourself to be irresponsible.

People injured in auto accidents often sue the drivers and other potentially liable parties. Your parents are potentially liable for any injuries you cause. Legally, then, their position makes sense.

Whether it makes sense in practical terms is another question entirely -- and not a question lawyers can help you with unless (maybe) you tell us a lot more about your circumstances. I can't estimate the risk that you will be in an accident. I also can't estimate the odds that they will be sued if you are, nor can I estimate the odds that such a lawsuit would exceed the amount of their liability insurance.