You ask a good question about the AM frequency response of the day. I want to say it was 20 - 7500hz but I don't recall the +/- db range. Seems it wasn't 1db, but 3 seems too extreme. Could it have been 2? The noise spec was -45 or -50db. Distortion limits were pretty high by today's standards...seems that the distortion limits were different at different frequencies? Maybe 3.5% at the low-mid frequencies and a little higher on the higher frequencies? Hopefully someone who was more into the AM side of things than I will recall the specifics. There was also a spec called Carrier Shift. I want to say that the carrier could not vary more than 5% between unmodulated and modulated conditions--chances are that rule still stands. Been a long time since I did an AM proof. Now what were people getting in real life? With an all tube transmitter into a dummy antenna at 1010 WCSI Columbus,Indiana in 1977, I was pretty proud of the numbers I was getting, so I remember them well : Frequency response was within +/1db 30 - 11000hz and -3db at 15000hz. Distortion was 0.5% at 400hz with 95% modulation and the noise level missed the FM spec by 1 db at -59db. It was a daytime station and I had the distortion analyzer on the transmitter every 2 weeks and kept these numbers consistently. And if I slacked off, the PD could hear the distortion starting to creep up...I had him spoiled.
The old 5 tube radios had far better high frequency response than today's AM radios...it seems 5khz response was pretty common with some getting closer to 8khz. There were a few AM tuners with a Wide/Narrow switch and in the Wide mode, they passed plenty of 10khz audio as evidenced by the 10khz whistle and/or the need for a 10khz whistle filter.
The car radios you speak of that ate the battery in the car had tubes in them and needed a couple hundred volts for the plates in the tubes. Getting 200 volts from a car battery was quite a challenge. The method of choice was to use a vibrator that reversed the polarity of the DC power into the transformer many times per second, effectively presenting the transformer with something that resembled AC power that it could use. Inefficient method, but it worked. Adding the filament power to that and you can see why the radio was quite power hungry. I was way too young to own a car in the 50's (and before) when these types of radios were common, but in the early 60's when I was getting interested in radio, I bought a few of them at auction sales for 25 or 50 cents and with the help of a car battery (thanks dad!), I got them to work. You could hear the vibrator purring if you listened closely to it.
Thanks for reminding me of some fond memories from the very dawn of my interest in radios that eventually led me to my broadcast engineering vocation!