How is volume not affected by signal strength in AM radio?
AM signal has a good reference - the carrier. AM receivers are generally designed to have an automatic gain controlling circuit (=AGC) which tries to keep the DC voltage that's obtained by rectifying the carrier in the diode detector constant. It's quite possible that a distant station needs 1000x higher total power gain than another which is either strong or placed in the same city as the receiver.
The simplest crystal receivers do not have that gain control and with them the volume varies as you thought.
There's a variation of AM signal - the SSB - which doesn't have a carrier. If someone isn't talking right now, SSB signal is non-existent. Gain control must either be manual or cleverly increase the gain slowly if nothing is detected until either the noise jumps too high or some strong signal appears.
FM radio signal has a carrier. AGC is used to adjust the signal level to be suitable for the FM demodulator circuit.