Why does FM sound better than AM?

I don’t buy this explanation. The FM modulation uses a much higher bandwidth than AM. The distance between channels on FM radio is 200 kHz compared to only 9 kHz on AM. That’s more than 20x more bandwidth for FM. On AM, no matter how deeply you modulate the carrier, the bandwidth will not exceed twice the bandwidth of the input signal. On FM, the deeper you modulate it, the wider the output spectrum will be, and it can easily exceed the bandwidth of the input signal.

In addition to that, the whole FM band is much higher frequency, while I guess quite a lot of noise, especially burst noise caused by eg thunderstorms is relatively low frequency. So it’s not picked up because it’s out of band.

Any noise that falls inside the channel does get picked up by the receiver regardless of modulation. However because the available bandwidth is so much higher than the real bandwidth of the useful signal, there is actually way more information redundancy in FM encoding, so this allows to remove random noise as it will likely cancel out.

If I encoded the same signal onto 20 separate AM channels and then averaged the output from all of them (or better - use median filter) that would cancel most of random noise just as well.

Also another thing with modulation might be that if there is any narrow-band non-white noise happening to fall inside the channel (eg a distant sender on colliding frequency), on AM it will be translated as-is to the audible band and you’ll hear it as a single tone. On FM demodulation it will be spread across the whole output signal spectrum, so it will be perceived quieter and nicer by human ear, even if its total energy is the same. That’s why AM does those funny sounds when tuning, but FM does not.

Neither is true. 9kHz, with two sidebands, means that the transmitted audio is limited to 4.5kHz, which is way too low to sound good. It was this, and not the noise, that made it sound much worse.

While one reason for limiting the audio bandwidth to 4.5 kHz was to allow a great enough number of channels in the long wave and medium wave bands, the second reason was to be able to reject the high frequency noise by low-pass filtering.

So there were two reasons for the low audio fidelity of AM broadcasting, and noise was one of them, with the contention between multiple broadcasters for the narrow available bands being the other.