If you are responsible enough to drive it, you can help foot the bill.
Car insurance is a requirement to drive. Our young adults need to get use to the idea of bills. And this is an easy way to begin the process. Of course they will need a part time job of some sorts. Great motivator, no job no money, no money no insurance, no insurance mom said I can not drive. This will also tell you the responsibility level of your young adult. America has enough irresponsible drivers on the road, lets not put out teens out there before they are ready.
Now when I say teens should pay I do not mean all of it. Not in the beginning anyway. I believe you should have an amount predetermined as to what your teen should pay and you foot the rest of the insurance bill. And let it be known, if anything happens, wreck or ticket, that increases the premium they will be responsible pay the increase.
After all every action has a reaction. Little Johnny gets ticket, goes to court pays fine, insurance increases he gets that too. He just had his first experience with real life and will remember it very well. Every one remembers the experience that hit them in their back pocket, makes you think twice.
Driving is a big responsibility and with it comes big insurance bills. It is an good opportunity to expose your teen to real life while still in your care. And teach them the right way to go about it. Such a the importance of paying the bill on time. Doing this will get them use to the idea and get them in the habit of paying on time. Later when they are older a second though wont be given to due dates of bill thus helping keep their credit good.
In essence teens helping pay the insurance do many things, it is more than just money. You are teaching necessary life lessons to your young adult. And trust me it is far less costly to teach those lessons now while they are still at home than to let them learn by trail and error after they move out.