> why don’t more games run their audio at 32768 Hz, if that’s such a natural rate to run audio?

I've written some code to play back 8-bit samples (and indeed to wavetable, FM, and VA synthesis) on 8-bit Arduinos using the PWM to output 8-bit audio. That runs at 31373Hz which is a pretty crazy sample rate.

Why?

Because the chip is clocked at 16MHz, and if you program the PWM for no prescaler and "phase correct" PWM where it counts up and back down, so you get a widening pulse in the middle of a "burst", then it counts 510 "steps" of the counter. It's an 8-bit counter so it counts from 0 to 255, then the next step counts back down to 254, and so to 0 again, when the next step takes it to 1.

And 16000000/510 is 31372.55 ;-)