Frequency does not diminish with the inverse square law, as does the amplitude of a wave that is broadcast in all directions. This is because frequency is related to a count of events over time.
Frequency from a source light years away is intact; we can look at frequency bands from a radiating celestial body and know which chemical elements there are, and also tell exactly how fast it is moving away from us from the red shift in that spectral pattern.
Be all that as it may, AM should sound great when you are close to the radio tower, and have ideal reception with no multi-path reflections, and good signal/noise ratio.
It still doesn't sound good, and that simply because of the bandwidth allocated to it is low. Furthermore, AM Stereo is a retrofit and crams two channels into one via phase modulation.
AM stations are separated only by 10 kHz, as you can see on your AM tuner (which you likely have only in your car, if that). The bandwidth is directly related to the audio bandwidth because modulation produces side bands.
For instance, if we modulate the amplitude of a 650 kHz carrier with a 1 kHz audio tone, we get side bands of 651 kHz and 649 kHz. You see where this is going? We can only go up to 5 kHz before we bump into the next station, which also needs +/- 5 kHz for its side bands.
This 5 kHz limitation is why AM radio sounds like your speakers have a heavy woolen blanket over them. It's almost as bad as the bandwidth limitation as narrow band phone calls. Listening to AM music is almost as bad as listening to on-hold music over a narrow band codec like G.711.
The kicker is that only one side band is needed to reconstruct the signal, so in theory AM stations could have 10 kHz bandwith. Unfortunately, SSB was not deployed for broadcast AM, even though it was already known at the dawn of radio.
(https://en.wikipedia.org/wiki/Single-sideband_modulation has a note about why)