These cars aren't prizes. They are parts of the "secrets" that belong to a small number of contestants compared to the total number of contestants. Not every "secret" was directly involved with automobiles.
These very early "panel shows" featured a usually repeating cast of panelists that would meet each week to try to guess the "secret," or in the case of "What's My Line?," the occupation of the contestant or group of contestants. So, an example of a "secret" that would have cause to bring a vehicle on stage would be "My father built this car in 1896." After the "secret" is revealed, the vehicle would be brought into view as more about it was explained.

Antp, I just wanted to make sure after discussing the merits of the "The New Price Is Right" listing. My show seems okay.