Unlike FM it doesn't suffer from the "Capture Effect" so you can tell if a weaker signal is trying to get through on a busy channel. And unlike FM it doesn't suffer from the Threshold Effect where weak signals suddenly disappear into the noise.

And of course Digital modulation is ruled out by both of the above considerations.

The only mode which is more efficient (for weak signal communications) is Single Sideband, and that can't be used in aircraft due to Doppler shift.

It is true that local reception sites can help, but they are not possible over water. Perhaps one day satellite systems might finally replace aircraft AM. The problem at present is the cost for fitting to light aircraft.