I seem to remember that Chrysler offered an all-transistor Philco radio for the 1956 model year. The radio was an approximately $150.00 option. In 1957, Chrysler switched back to hybrid tube / transistor radios. I believe that transistors were commercialized in 1947 or so but were used almost exclusively in military or other high tech products due to their expense. This is why the battery tube portables lasted through about 1955. They were much cheaper than transistor radios but obviously the batteries were more expensive. What the break-even point in hours used was, I don't know.
Below is a link to the "Allpar" website and a good article on the Chrysler - Philco car radio.
https://www.allpar.com/threads/1955-chry...0available
When I was a kid, my friends and I used too "scrounge" at the town dump. Due to the low worth of scrap metal, a lot of abandoned cars were merely discarded at the town dump. Since this was around 1969-1972, I never found a 1963 car, as newer cars went to Junkyards. We collected quite a few car radios, which I wish that I still had.
Most car companies offered "transistor powered" radios starting in 1958 when "Space Charge " replacements for the 12BE6, 12BA6 and 12AV6 were made available, I believe by Tung Sol. These tubes could operate well with a 12V B+. However, no power output tube was available that could run on a 12V power supply and replace 12AQ5s or 12V6 tubes used at the time, therefore a single or push-pull power transistor amp was used.
GM offered a "trans-portable" car radio that had a battery powered all transistor portable radio located in the Dash on the 1959 Pontiac and Buick This could be slid out and taken to the beach. There were connections to the car antenna and 2 transistor power amp for the car speaker. This radio had no push buttons, only the volume and tuning knobs. Oldsmobile went one step further. Their portable, offered in 1958 and 1959 was much lighter, as it resided in a sleeve in the glove box, hidden. The dash contained a "head" with the typical volume and tuning controls, the typical "slide rule" tuning scale and push buttons. The Dash radio required the portable radio to be in place in order to operate. I have to assume that the dash component had a power amp for the car speakers but I don't know if there was any active electronics in the "head", or if so, did it act as an RF and Convertor and only the IF, detector and audio sections of the radio were used. A very interesting concept. GM did a lot of interesting things in the 1950 and 60s. The Corvair and 1963 Tempest are examples.
Most car companies migrated from these "hybrid" radios to all-transistor radios by the 1963 model year. Ford used all-transistor radios in Lincoln and Thunderbird models since 1961. I remember them to have a higher distortion than tube radios. They mainly used germanium transistors.
If you google GM trans-Portable, you will see articles and You Tube videos on that subject.