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I think commercial AM radio developed in the .5-1.6 MHz spectrum because the equipment was easy to construct for that spectrum. Also it was found that frequencies up to 10 or 15 MHz are able to 'skip' high in Earth's atmosphere, to be picked up thousands of miles away. This was a major advantage in the early days of radio.
Commercial FM broadcasts have good sound fidelity. The carrier needs to modulate the audio spectrum (15 kHz), therefore the carrier frequency needs to be many times faster than 15 kHz. I don't know how they determined what minimum frequency would be satisfactory, whether it should be 1M Hz, or 10M, or 100M.
I agree that when AM radio was invented then it was difficult to make circuits work at frequencies higher than 2MHz (2000kHz) so 540kHz to 1600kHz frequencies were used.
The very high frequency used by FM stations avoids interference from other radio services and static from car ignition and other interference. Also its antenna length is fairly short.
My model airplanes are controlled with digital signals at 2.4GHz. I think 40 of them can be active at the same time and automatically avoid interference between them.
The AM band runs from 300 kHz to 27MHz. The range is not continuous but is divided into several band. There is a LF band (rarely used) and a medium frequency and a number of shortwave bands. For AM (SW) radio, bands were usually designated by wavelengths, e.g., 13M band, 47M band etc.
The same spectrum was shared by defense, police, airplanes etc. In addition, considerations like atmospheric reflections were also considered.
Aircraft and their control towers use AM so that another party can "break in" and say Mayday, my airplane is on fire! They operate on frequencies (108MHz to 136MHz) above the FM broadcast band. FM has a spec called "capture ratio" where it takes a strong signal to break in at the same frequency as an existing signal.