That "sound" is partially due to the design of the current AM system. It was built to pack more transmitters into the allocated frequency range.
There are no technical impediments to high fidelity audio because of amplitude modulation. In the past the big limitation was the bandwidth of intermediate frequency (IF) amplifiers in the receivers which were typically tuned for maximum gain and not flat audio band response. The transmitters have flat response out to the legal limits. Radio stations have a monitor receiver that has proper IF audio response and the sound of those are very good.
That's he-aac so 56kpbs is not that bad, it gets dicey below 32kbps when you need tricks like parametric stereo. But he-aac's spectral band replication does add metallic taste to everything, i would agree
AM only has lower fidelity because of the low broadcast power and shitty receivers. 80 years it was much higher quality with the huge transmitters and high quality tube radio.
"Most European countries are now running a reduced AM radio service with fewer transmitters, fewer services and
lower power. Albania, Andorra, Austria, Belarus, Belgium, Croatia, Estonia, Finland, Norway (except Svalbard),
Slovakia, Sweden and Switzerland have completely closed their AM radio services. Denmark retains a part-time
long wave service for mariners. Lithuania has closed domestic AM radio, but retains a medium wave transmitter
for international broadcasting. Only Cyprus, Hungary, Iceland and Romania (together with England, Scotland,
Wales, Northern Ireland and Spain) are continuing with a comprehensive AM radio service."
This is outdated. Denmark closed its long wave transmitter last year. The biggest hold out is bbc radio 4 and they stopped special long wave programming and the service is only still on the air because it doubles as a digital signal for some power meters.
Most European countries have switched off all their major transmitters, or are preparing to switch off the last few that are left. E.g., in the Netherlands, there are now only low-power hobbyist stations, which will remain I think, but have a near-zero audience.
Long wave is a frequency band just like medium wave. Amplitude modulation is used on both; it's the same technology, LW needs much larger antennas though. FM is often used to refer to a frequency band, but that is actually called ultra-short wave, and frequency modulation is used on it.