Why is it possible to have undistorted power amplifiers?
The magical term is "negative feedback". Even with nonlinear amplifiers the overall feedback from the output to an error amplifier can correct these nonlinearities. This can result in highly linear systems, even when the individual compontents are not.

You can think of it like this:
The output amplitude is scaled to the level of the input signal (a simple resistor divider has barely any problems with nonlinearity) and is feed back to the input stage. There this down-scaled output signal is compared with the input signal. If they don't match, the input stage can correct the output and by that eliminate the distortion.






simulate this circuit &ndash; Schematic created using CircuitLab

In the schematic above the feedback is 1:1, it is not scaled down. This means the output voltage will be the same as the input voltage, but you can draw a lot more current.
If you would put a 2:1 voltage divider in the feedback path, the output voltage would be double the input voltage.