As Walt mentioned, the ability of an AM transmitter to pass a square wave without tilt or ringing was/ is important. Then, the antenna system needs to pass the all the frequencies in the modulation bandwidth without too much phase or level shift. During that era clipping was the method of final peak control after gain reduction from AGC and limiters. The clipping made square waves that established the maximum peak level. If the peak level of the square wave was changed by the transmitter or antenna, modulation/loudness would have to be reduced to prevent overmudulation.
The Volumax had a diode to clip the audio. It was inside epoxy and called the "polarity sensor". Until the 125 percent rule was in place, the polarity sensor only clipped one side of the audio. Properly phased with the transmitter, the positive peaks from asymmetrical audio would be unclipped and could go as high as they wanted to (if the transmitter and antenna were capable of it). After the 125 rule was effective, a new polarity sensor was available that clipped both sides, one 25 percent higher.
Stations with transmitters capable of passing a decent square wave and good wide antenna systems could sound great and modulate hard.
Now, I believe all new AM transmitters pass square waves reasonably well. Antennas are what they are, some excellent, some not so good.
I know many here know all this very well, I mention it as background info for those who are not from the era.