And the less efficiency you will need in your speaker, aka transducer.
At these conditions there is also no more need for user-supplied power for the audio output to become audible, so no electronic amplification is needed.
As you get closer to the source the need for a carefully crafted, somewhat complex, receiver circuit will diminish, and when there is only one audio program being broadcast on a single radio frequency, no need to discriminate between different frequencies.
In an electronic radio, after the single radio frequency channel has been selected, then the radio frequencies are filtered out before electronic gain is applied to the audio alone. Otherwise audio power would be wasted amplifying radio frequencies that are not audible.
The hot dog emulates all of these requirements, except for the receiver sensitivity that would be needed to respond very strongly from a distance. No noticeable demodulation until it touches the source directly.
Then as a single-component device, a low-efficiency transducer, it conducts the full undemodulated RF power.
Its frequency response as a transducer is probably not even as high as human hearing can go, and people can not hear any RF being reproduced anyway, so all you hear is the audio.
Plus when it comes to hot dog conductivity, who could forget this futuristic home appliance from the 1960's:
Amy demonstrates the Presto Hot Dogger
With any modulation scheme, you have the "carrier signal" and the "message signal." The carrier is the frequency you dial into your radio. The message is the thing you listen to - voice, music, whatever. Those two get "modulated" together and blasted out over an antenna, and ta-daa, radio!
Amplitude Modulation is really, really simple. It's literally just the product of the carrier signal by the message signal. The carrier signal is a really high frequency relative to the message, which is where I'm guessing the "resolution" of the signal comes from.
Now, hot dogs.
Hot dogs probably don't resonate very well. Or, maybe they do, but just a little bit at low-ish frequencies - up to a couple thousand Hertz, but no higher. If that's the case, then a hot dog would act like a low pass filter! Since AM is just the product of a high-frequency carrier and a low-frequency message, a low-pass filter could ostensibly leave behind something that resembles the message signal.
Proper AM demodulation involves diodes and whatnot, but I can't imagine a hot dog has semiconductive properties.
Now, if it's an electrical signal, why can we hear it through the hot dog? A hot dog is not a good antenna. It's bad at inducing an electromagnetic field around itself. Instead, it converts the energy from the radio tower into mechanical force - motion, like the way a speaker moves.
All of this could be wrong. Maybe the hot dog isn't serving as a filter, and it is indeed reproducing the AM carrier signal - it's just too high of a frequency for us to hear it. I don't remember my signal processing classes well enough to say for sure. Maybe my whole "hot dog is a speaker" explanation is bunk. Maybe hot dogs really are semiconductors. Not sure.