You’ll notice that as you go up in frequency, the amplitude of the sine wave changes at a greater rate than at lower frequencies
I think you may have made an error here, simply mis-spoke, or maybe just a little confusion to clear up???
Amplitude is usually defined as the Peak Value. In that usage, the amplitude (peak level) isn't changing. Rather, it is the slope that gets steeper at higher frequencies. Meaning that you hit your peak value faster, larger value of angular momentum in the phasor model.
Perhaps you meant to say that the instantaneous value is changing at a faster rate? That make sense.
May be a bit of splitting hairs, but want to be sure we are all on the same page.