It may sound crude, but it is pretty effective. They make sure that you mostly see things you're interested with, sprinkled with some other stuff - because a) you might find it important too, but they don't know, and b) everyone changes their interests from time to time.
[0] - Yes, there're options to signal "please don't show me this kind of stuff" or "don't show me stuff from this person", but I use them so rarely I don't really know if they work in any other way than just blacklisting the thing/person you pointed out.
[1] - I've noticed this directly after liking a post under a fanpage I basically never interacted with. I suddenly saw their posts everyday. Then every other day. Then every few days. Another like, and they're back to showing up daily for a while.
I don't like framing the issue in terms of "missing out". It leads to the "paradox of choice"-type worrying. There are always more interesting and fulfilling things to do than hours in a day. You seem to have developed a good social life framework for yourself that doesn't include Facebook, so I wouldn't say you're missing out.
As for stream, if mine looked like that I'd be unhappy too. You could probably clean up yours quickly though - just scroll through it and/or visit profile pages of some of your friends, and start "liking"/commenting on posts that you find interesting. Facebook filtering algos will quickly catch on your interest, and you'll be seeing much less crap.
RE etiquette, as far as I can tell you're correct; generally you accept people you met IRL, with rare exceptions of both kinds - sometimes you don't really like your new acquaintance, and other times you may decide to add someone you met on-line if you know them well enough already. At least that's how I myself and people I know use Facebook - maybe the culture is slightly different in other parts of the world. But the rule of thumb seems to be: if you think the person is OK and you might want to talk some more in the future, it's OK to send/accept a Facebook friendship invite.
> It just doesn't fulfill any purpose in my life and actively makes me angry.
That's totally fine and, IMO, a perfectly good reason to not use Facebook.