After 6 years with the Navy,  in 1977 I went  to work for the FAA as a technician for the next 33.  At that time, the first thing you do is start at page one no matter what your experience level with a correspondence course known as the DFF 100.  So, with 'This is an atom' ,  for the third time, got educated again in electronics.  After that, the next thing you do is communications, all the way back to Sam Morse and into spark and arc transmitters, crystal sets, regen, super regen, super hets, all the way  up to the current era.  The very first thing discussed when they finally got to voice modulation is AM over  FM  and a lot of research was done in this area by very  high level thinkers.  SSB was brought up,  and as this was even more complex than FM, dismissed entirely, but is still used in long distance overseas comm.   In black and white in the books I had, it said clearly, AM was used because of the simplicity of the receiver circuits, it offered of from of communication check sum in that two carriers made a heterodyne so you know somebody was interfered with and to repeat the message, and that the capture effect of FM was a risk factor.  AM was/is deemed 'safer'. Today, the simple diode detector is long gone, with much more complicated circuits and component level,  the freq stability in modern aviation gear is so good that most times you don't get a heterodyne, what you do get is similar to the old telco party line, you can hear two, or more people talking at once and you know to sort them out, and FM is still considered too risky.  Maybe the idea of AM vs FM will change on how to communicate with a plane, but nothing will be as simple and foolproof as plain AM.  Around 2010 the FAA decided they no longer needed the backup microwave link system that they had just spent tens of millions of our tax dollars on to update and make more reliable by adding more repeater sites, a system that was  spread out all over the country.  Now, they put all their eggs in the telco basket, the modern FAA is known to take chances to save a buck, just hope you are not in an aircraft when those go cheap ideas collapse. 

Charlie in NC