Driving is an incredibly unsafe activity. If it was just dangerous to the driver, then I wouldn't care, but it becomes dangerous to everyone else. You want to know that your airplane pilot is licensed just like you want to know that the other cars on the road are..which is worth the minor hassle of having to get licensed yourself.
It's not that burdensome to take the DMV test..it takes, what, 10 minutes? I don't want 13 year olds driving on the freeway at 90 miles per hour, I'm sorry.
I'd raise it to 18, just to match a universal age of adulthood.
But the consequences are so great that people will think twice.
You overestimate people.