Did car manufacturers ever offer the option of an in-car phonograph? I would have thought not. After all, the technological challenge presented by such a product is obvious. How can you get it not to skip? But trusting in the common sense of car manufacturers is never a wise thing to do. So in this respect it's probably obvious that, yes, such a feature was once offered, though for a very brief period of time. Predictably, the in-car phonographs skipped like crazy and were pulled from the market.
Ookworld.com offers a history of the Highway Hi-Fi
. They debuted in 1956 as an option in some Chrysler models. The big catch was that they only played records specially made for in-car phonographs: 7-inch 16⅔-rpm ultra-microgroove format records. There were only six discs in this format to choose from. Those discs contained a selection of "classical recording, the tops in popular music, drama, children's stories" selected by Columbia Records executives.
Chrysler didn't offer this style of in-car phonograph again. But in 1960 it did offer a unit that played regular 45-rpm records. You could stack up 12 of them at a time. It worked well if you were sitting in your car idling. As soon as the car started to move, there were problems.
The UAW-Daimler-Chrysler site
also offers a shorter history of the in-car phonograph, with color pictures.