Yes, but that use case is a different setup for each person who wants something like it. The typical case of one person with a speaker and headset attached is common enough that some heuristics can make the right thing happen for most people all the time.

You need a program that can setup the output graph manually. These are aimed at the home recording studio market as they are the majority of users for that type of thing.

Yes, trivially. Or other things. I even route the output of Spotify into Google meet as my microphone for meeting I tro/hold music, though watch out for noise canceling algos :)

Example - https://kx.studio/Applications:Catia