kw5kw,
If a person keeps car doors locked and the gun on the seat or between the seat & console, access is much easier than if its on your body strapped in the seatbelt with you.
I can see your point about the locked box under the seat, but I think that is for locking up the gun when you need to go in a forbidden location (schools, polling places, etc.).
Since I teach at a school, I plan on getting a locked box for under my seat for when I'm teaching. I don't like the idea that a kid could throw a brick through my window, find my gun, and then become a school shooter with MY GUN! I don't think the locked box is for keeping while someone's just on the road.
As for what you've said about ladies carrying in their purses, I completely agree. I don't carry in my purse for that very reason. I don't want to arm a criminal. I carry on my body. If someone gets my gun off my body, they've gotten pretty intimate with me. About the only person allowed to get that close is dh, and possibly my mother if she's checking under my shirt to see how much weight I've lost. (Mom's are allowed to do things the average citizen can't.)