I honestly don't think the game you want has been made yet.
The closest thing I can think of would be <strike>Motostorm: Apocalypse.</strike> No I take that back.
What you want is Burnout Paradise. Open world, lots of cars and mayhem. Similar arcade driving physics. Customization is limited to paint color, sadly. But that would be the closest thing to what you are asking for.
The only thing that bugged me about it was a lack of story.
