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I think we had some fairly recent discussion on HN since I remember commenting.

As you're saying, it's about bandwidth and signal to noise. Not something inherent to modulation.

The modulation is important. FM is more robust against external noise than AM.

Only while signals are strong. On weak signals however, AM has a considerable benefit in intelligibility over FM.

FM stays good as the signal weakens, and then kind of drops off a cliff almost.