To help you understand, imagine 1-bit audio. What would it sound like? For each frequency, you can only have a single volume, i.e. it's maximally compressed.

I'm not sure the 1-bit extreme helps with understanding this, particularly because the audio we'd be dealing with will be a mix of many frequencies; the waveform is an aggregate of the overall 'signal' at each frequency present in the mix; this is one of the reasons why multiband rather than single-band compression has become so popular (as it allows you to get the 'max' in each frequency band rather than one band dominating the overall result of the compression).

I think there's a difference to take into account when considering any given momentary sample and the overall effect - yes, compression does reduce the dynamic range of the music, but you would need some sort of variable bit depth which was linked to the instantaneous amount of compression being applied to get any kind of workable lower-bit-depth encoding scheme, which seems like a lot of complexity for no significant gain (to me?).

> Compression means it's effectively using less of the [dynamic] range and the dynamics [range] could be represented with fewer bits in an optimal encoding.

Lower DNR can indeed be encoded with fewer bits per sample.

The meme "Math class is hard, let's go shopping" is only slightly apocryphal. Two of the voicebox lines were "Math class is tough" and "Want to go shopping?"

Because we only have 8 bits per channel, we all can see banding in (dynamically) compressed images. That's what increasing the depth improves.