The accusative case in guteN indeed comes from wishing it for the other (English is grammatically not expressive enough here).

This is the same BTW in Hungarian. Even better, in HU we still have the form of "I wish (you) a good{Acc} morning", however a bit less formal way you can say just "a good{Acc} morning"

This simplification happened to German earlier too. In fact, my German old lady neighbor still to this day says every time: "Ich wünsche Ihnen einen guten Morgen / schönen Tag, Herr kmarc"

Yes and no. It does come from the longform well-wishing but it has been a separate greeting for a decently long time which is reflected by the fact that "guten Morgen" became "Guten Morgen" in the spelling reform 25 years ago. (Though, they did allow both variants a decade later (as is the case with a lot of other words), "Guten Morgen" is still the recommended one.) So that means if you are wishing someone a good morning, you are wishing someone a good morning + greeting. If it is just a good morning, it really is just a good morning (for you) + greeting. I do use both variants but actually wishing someone well is more reserved for people I've been interacting with for a long time (like certain cashiers in a supermarket (if there is time) or employees of a bakery), really friendly strangers or special cases (like someone is being a dick and one is being sarcastic).

The fact that you need 25 years of cultural background to understand what Guten Morgen means is the whole point. You could similarly explain why Americans asking "how are you" is not a real question; the whole point is that the culture differs from the literal phrase, which makes it difficult for non-native speakers.

Not sure why you downvote me for explaining why the language used by an old woman is not indicative of how things are today (or have been for a while even). (Though, in her case, in kmarc's example, the usage of the longform makes sense regardless.) Apart from that, we discussed German terms, not American ones. And, as explained, in German the discussed greetings are actually taken rather literally. At least I believe giving some very small insight into a culture is actually useful but apparently you disagree.

Taken literally? Well, then for "Grüss Gott" I would have to literally believe in god, then die and be lucky enough to go to heaven and greet god there (provided I'd get an audience). I think greetings are a meaningless formality anywhere, just learn them and the expected answers by heart and ignore the meaning.

Please re-read what I wrote. The sentence in question: "And, as explained, in German the discussed greetings are actually taken rather literally."

This is exactly how "How are you?" is meant in American culture. It's not fake; greetings are culturally determined and especially the most common greeting phrases in any culture should not be treated literally but instead as part of a ritual exchange.

"How are you?"

"I'm well, and you?"

"Great, thanks."

It's just a ritualistic exchange.

See also the English upper-class ritual introductory exchange:

How do you do?

To which the correct response is:

How do you do?

I’ve learned, can’t say if mistakenly or not, that if an American/Brit really expects you to answer, they will say “Are you OK?”

The Japanese say something like "nice weather, eh?" (ii otenki desu ne? - to which one replies "sure is! - "so desu ne!") -- which is mostly just a semantically little-analyzed pragmatic sequence functioning as a casual greeting.

It’s also not universally American. One of the adjustments I had to make in Boston is “how you doin’?” being the start of a leisurely conversation instead of a quick pleasantry.

It's not just American. It's very similar at least in Belgium and I suppose on other western countries too