Humor can't really be taught, expect by life experiences. So, you either have it or don't. And the same goes for specific kinds of humor. Some people can't get irony, or black humor, or the fun in puns, or other kinds. That doesn't mean they can't find the humor in other genres.
From your comment, it seems like you overanalyze it. You talk about whether:
"[it's] supposed to profoundly compare pure happiness versus struggle for progress"
-- as if you expected some profound philosophical revelation/insight from it.
No, it's not supposed to "profoundly compare pure happiness versus struggle for progress". It's supposed to make a tongue in cheek comment about "pure happiness versus struggle for progress". And about how "progress" is not the be all end all.
It's not supposed to say something so profound that people haven't thought of before, or which is deeply philosophical and goes to the core of our being.
Just to say things that a lot of us have felt/thought, about the futility of certain pursuits or how some achievements turn out not to be that great after all, in a funny/casual manner.
As for the mechanics of the joke, it's the classic (found in countless jokes) reversal of premise and conclusion:
Men think they're smarter because they do X and dolphins do Y, dolphins think they're smarter for the same reasons.
Immediately this brings up the relativity of view points, and how interchangeable they can be.
Then it makes you consider the particular example, and how what we think achievements could just be BS busy work (or even actively harmful to us enjoying our short lives). Not in a "what a deep insight / discovery", but in a "yeah, it might be silly, but I sure felt like that some times too".
Then there's the listing of the achievements (mere well crafted listings can be a source of humor in themselves, e.g.: https://en.wikipedia.org/wiki/Celestial_Emporium_of_Benevole... ). It goes from something most would agree as good (the wheel), to something subjective (New York), to something inherently bad (wars) but nonetheless a mark of our "progress" as species (animals might fight, but they don't do wars).
>...or take the whole babel fish thing; Why a fish for translation?
Now that's more the ocd you talked about. Why not a fish? It can be small (consider something like a goldfish), and has a shape not that bad for fitting into one's ear. And it's a living organism (so not inorganic rock which wouldn't do the translation as good). What Adams primarily wanted to have there in his story was something organic (not a technical babel-gizmo), and that could fit an ear.
It could just as well have been a babel-worm, or babel-ant or something just as well, but fish was one good option, sounded friendly enough (better than a worm), a little out of place too (doesn't it need water?) and Adams took it.