While they do prompt contestants to go to the car on Price, it seems that some of the other "running over" instances are due to excitement and proximity.
Not that I enjoy forced enthusiasm, but his may be preferable to the former practice: (1) jump up and down, (2) kiss host, (3) get the hell out of host's shot. I can see why they'd encourage the run, at least to a car. It gives the winner more to do. The license plate holder is stupid, though.
It's something the show uses to accrue followers on Twitter in this world where likes and followers are king.
That's true, of course, but I wonder why this would interest anyone who isn't going, at least as long as it's items like mascara or a hair dryer and not bondage implements or naked photos. Then again, much of Twitter's appeal escapes me.