These are on the high side, but there are still instances in which they won’t be enough to fully cover you. For example, if you accidentally hit a luxury car, replacing it could easily cost more than the $25,000 legal minimum for property damage coverage. If the other driver is injured, his or her medical bills could also exceed the $30,000 bodily injury minimum fairly easily. In each case, you’d be responsible for making up the difference yourself.
Although we’re sure that you’re probably an excellent driver (you would never speed or cut someone off, would you?), and an even better parent, how are you as a teacher? Many driving school instructors have been teaching student drivers for decades, and we all know teenagers are more likely to listen to literally anyone else than take instruction from their parents.