"Shannon theorem disagrees with you. The wider the channel, the MORE noise you can tolerate when transmitting signal at a given data rate."I've spent a lot of time on the development of broadcast-quality FM exciters (as I've posted on HN in the past) but I'm not go to debate the disadvantages/advantages of FM versus AM in depth as most points have already been covered in other posts, I'll just add this:
The quality of AM can be remarkably good if it's engineered with care. The math and engineering tell us that, and excellent results can be and are achieved in practice (as a longtime FM-er I say that about AM as it's just fact)!
The reason why AM has a bad reputation is it's history and background: AM broadcast and other shortwave (3-30MHz) bands are much more prone to impulse and atmospheric noise than VHF and up. Also, the historical nature of RF amp design and detection never put its primary focus on the linearity of RF/IF amps, etc. (good linearity is easily achievable these days).
My primarily reason for responding to this part of your post is to point out that when receiving AM signals one can take excellent advantage of using a wider bandwidth than the actual spectrum occupied by the modulation products.
Unfortunately, most of us don't know or have forgotten about the Lamb Noise Silencer circuit which uses a wider bandwidth signal to gate out impulse noise.
Here, two IF amplifiers [or one especially modified] are employed. The main IF uses the required (narrow) channel bandwidth and the second IF uses a wider bandwidth. Shannon et al tell us the wider signal can arrive at the detector before the narrow BW signal and thus can be used gate out noise in the latter stages and or detector.
In operation a properly designed Lamb Noise Silencer is remarkably effective in reducing AM static etc.
Whilst never used as a broadcast service, I'd posit that if AM with say 20Hz-20kHz audio were put into the existing FM spectrum (88-108MHz) with its lower AM noise background together with receivers that used the Lamb circuit then AM would essentially be indistinguishable in quality from the existing FM service. In fact, it could be even better with audio reaching 20kHz [extra 5kHz] and this could be achieved with a much better utilization of the spectrum (with AM's inherently lower channel bandwidth)—many more stations could be added to the band.
Of course, that would have been impractical back 80 or so years ago when the FM band was conceived for reasons that in the days of tubes the required local oscillator stability would have been very difficult to achieve (but a non issue these days).
Sometimes, we overlook the fact that our predecessors have already been there, thought about and have done these things.