It's just a bad idea
Um ... okay, try this. In the spirit of bananas and pickles, of course.
My daughter is seven. And she's pretty smart, I think. But once in a while, she just walks up to me and hits me. Punches me. Clocks me with a stick, drills me with a ball. There's nothing malicious about it. She's just caught up in what she's doing.
And here's the thing: It's expected behavior.
Right, all sorts of considerations about that, but they're beside the point for the moment.
What I'm getting at is that acutely irrational and spontaneous behavior is an expected part of her conduct in a way adults are supposed to learn to suppress.
Additionally, as any parent at this subforum will attest, children at age seven, or ten, and even twelve or thirteen, are nearly multivalent in their stream of consciousness; their attention can change focus drastically, quite literally, in mid-sentence. And it happens a lot.
No. I'm not putting a thirty-five hundred pound car in her independent control. Not now, not at ten; not a day before the law says I can, and I think, all things considered, the law probably says go too soon.
I don't want my daughter to have that kind of mortal responsibility in her hands at age ten. I have not prepared her psyche for that. Very few parents have prepared their children's psyches for that. Even those who take their kids hunting aren't putting such a sustained burden on their consciences.
I also think we would be turning Darwin in his grave, so to speak. What trends would having children driving cars bring to natural selection?