So this is precisely what it looks like: A car with a record player mounted under the dash. They were popular options in the 1950s when clear channel radio stations were still limited and when commuting from your nascent suburban community into the city for work was still new and exciting. The Philips version pictured above-bottom seems to work a bit like a CD player in that it sucks the disc in, but most of the devices required drivers to actually drop the needle on the record. Since we can hardly be trusted to keep control of our cocktail while flipping the record (much less positioning the needle), this seems like a particularly bad idea.
File this alongside the SPCA-unapproved dog riding sack in the "History of Bad Ideas: The Eisenhower Years"