"simplicity is better for play.. Just not for driving."
I faced this same issue, but eventually came to realize how to make it work, at least for me.
First off, how often have we seen someone on the road "lost in thought" and not paying attention? Yes, they seem to be driving just fine, until they drift out of the lane (which they correct with a jerk to the wheel) or they sit at a stop light and not notice the light has turned green? Being on "automatic" (unconscious) is not necessarily all that great.
The trick I found is not to let my mind wander. This does not mean to concentrate on any one thing (such as the gas pedal). Instead, I just drive "aware" with my mind clear. I admit I "clear" my mind by noticing something such as the vibration of the car as it moves (something general -- easy to notice, not specific such as the action of my foot on the brake).
No, I don't do this all the time because overall my discipline is pretty meager. However, I notice that when I have my family in the car I'm much more prone to "drive with the car" where when I'm driving alone, too often I'm totally automatic (lost in thought - coming to, every once in awhile).
I wasn't able to do this in the car until I had practiced sitting (zazen) for some time. Before I had enough experience just sitting still and being very aware (lots of headaches!), when I had tried it in the car I found myself making an increased number of little mistakes. It was almost as if trying to be aware, made me less aware. Works fine now and has even made "simply driving" a bit more fun and enjoyable.