Eric, i thought feedback was something to create the gain. I am too far from this field, but will try to have a look on some books (e.g. why the feedback is unavoidable).
Could something similar to switching waveform be used to create a correct and accurate digital signal from the source analog signal and "amply it digitally" without any distortion? Is there no way to amplify a digital signal directly from the digital sources (e.g., CD player), what this would really mean? Then you will again need a DAC just to output the amplified digital signal to the speakers (but i understand that "amplified digital signal" cannot exist, a binary number cannot be amplified and that that the conventional amplification is analog).
You can have gain without feedback. There are class A, AB and D amplifiers that use no feedback.
The problem with what you propose in the 2nd paragraph above is that digital audio switches at speeds far too low to be practical to amplify directly, and at some point you do have to create an analog signal to drive your loudspeakers. So what some products do is they accept the digital input and then convert the switching of the digital to a much higher frequency that is practical for a switching power amp. Some amount of DSP is required for this approach. But a switching amplifier itself is an analog process plain and simple.