The primary selection criteria for choosing FM vs. AM is dynamic range
There is no fundamental reason why AM cannot support the same dynamic range as FM.  You can vary the amplitude of a carrier over as wide a range as you can deviate its frequency.  The fundamental limitation on dynamic range of any information carrying medium is noise. In this respect, FM can be superior to AM but the tradeoff is bandwidth.  An FM signal will have a better signal-to-noise ratio than AM (hence the better performance of commercial FM broadcasts than AM) but at the cost of greater bandwidth. Sending a 1 kHz signal with AM requires a bandwidth of about 2 kHz.  Using commercial FM requires about 150 kHz. You can't get something for nothing.