On the contrary, quantization does occur in class D amps.
It is not quantized to something like 64,000 or 4,000,000,000
levels (probably what you're thinking of); it is quantized to 2 levels.
The output voltage is compared to the input voltage (using
some circuitry for scaling the voltage) to determine which is
greater. The result of this comparison is "true" or "false" -
the discrete results required of a digital system. That result
is used to determine if the output signal should be pumped
more positive or more negative.
This comparison is quantization. Don't believe me?
Check the Wikipedia definition.
"Quantization, in mathematics and digital signal processing,
is the process of mapping a large set of input values to a
smaller set."
I'm not making this stuff up.
I agree with that. There are steps in the process that are digital. I would have to ask the same question, though:
What digital code is representing the signal at any particular point in time?
Keeping in mind that the output is analog and unquantized, how is this represented as a unique set of logic levels?