You can have lots of weird cars like that in the US too, but only as long as you START with a normal car and then mess with it. Most states don't have anything like the MOT (or if they do, they only check emissions and nothing to do with safety), so once the car is originally registered as a VW Golf or whatever, what you do with it after that is your own business.

As is typical with US regulation, it's a "worst of all worlds" hodgepodge that makes no logical sense.