I mean it sincerely. Are you listening to something else while using a website with sound? I usually just pause the music.

If it's some music/podcast isn't it more handy to have a known volume knob on that instead of finding one on every website?

I don't care about the right opinion. I'm just curious about scenarios where lack of volume control is a problem.

Hear, hear.

I know where my computer's volume controls are - and if I have a keyboard with volume controls, that's what they work on. I almost never want to touch a specific app's or website's volume control... unless its volume is way too soft even at max system volume.

Basically, I don't need a gazillion interfaces. One suffices. Just don't go out of your way to make that generic, system-wide interface insufficient for your app and it'll be fine.

Suppose you use different apps that output sound. I use audacious, Firefox (Youtube) and mplayer on a regular basis. All these have their own volumes adjusted at different levels. Having a single volume isn't good enough. One app would be too loud and another too quiet. Plus I'm used to being able to change the volume on one app without affecting the others. Not having this control would be annoying.

I think you answered your own question. Not everyone needs just a single audio-playing app at the same time.

Audio is also things like warning sounds, it isn't just music and games.

Yes, discord and twitch stream at minimum.

Hmmm, pulseaudio volume control allow me to change the volume and device used for every single source (app, firefox tab...) I am running.