Poll results! The vast majority of you (70%) said “good afternoon” sounds more formal than “good morning.” A few people didn’t have a preference, but not one person said “good morning” sounds more formal. For the record, I agree with the majority here.
Okay. So what was the point of that?
The first and biggest point is that words and phrases have many shades of meaning beyond what’s in their dictionary entries. Nothing about the words “afternoon,” “morning,” or “good,” suggests any particular degree of formality, yet somehow “good afternoon” does. Why? I don’t know. I’m sure there’s a history there, something that research could probably uncover. That’s not the point. The point is that the extra meaning is there, seemingly without reason, and you as a writer are responsible for knowing about it.
Other examples are endless. “Good day” sounds (to my ear) even more formal than “good afternoon,” though again, I couldn’t say why. If a character gets a phone call asking for Samantha, it says something different about her as a person if she answers “That’s me” versus “This is she.”
It’s not just about degrees of formality, of course. You evoke other stories and events by your word choices. For instance, you can never, ever say “final solution” – no matter how logical the phrase may be in context – without evoking Hitler. You can never use the words “gospel” or “crucify” without reminding people of Jesus. The word “columbine” means “dove-colored,” but for anyone born before 1999, it’s going to mean something else, too. If you start a chapter with the phrase “Call me [character name],” you’re referencing Moby-Dick. If you use the phrase “ineluctable modality” (as I so often do in conversation) then all of a sudden you’re talking about Ulysses.
If you use words like “proletariat” and “bourgeois,” people will wonder why you’re talking about Marxism. If you say “towards” instead of “toward,” you’re signalling that you prefer British usage to American. In the book Kraken that I’m reading now, the author China Mieville uses the nonstandard “alright” instead of the more proper “all right,” which is a sign to the reader that the book will be something a little different, a little relaxed and not bound too tight by convention (even though he uses words like “aleatory” later on).
Okay, this is turning into a longer post than I expected, and I’m running out of time this morning. I actually have other points to make besides just “words have shades of meaning.” Hold those thoughts! I’ll come back tomorrow and finish.
Brian D. Buckley 
I would say that the difference between “good morning”, “good night”, and “good day” is mostly frequency of usage. Chances are you are going to hear good morning most every day, but it is rare when I hear the other two since people don’t use them often even when appropriate. It seems to make a sprial with some words and phrases as they are less used as they sound more formal and sound more formal as they are less used.
A vicious circle of formality…interesting idea. If that’s true, though, how did it start? I would think all three are useful expressions that would have no reason to begin dying out. “Buenos dias,” or “good day” in Spanish, still seems to be going strong.
Obviously we can’t know how these things start. It’s not like there was a person cataloging how often different phrases were being said and speculating why trends might be changing. It really only shows up when one generation realizes the previous does something a different way and goes “oh that is just too ____”
But if I were to do my best guess it is because either a) we live in a lazy society, or if you have a better view of humanity b) the diversity of English language speakers.
English society, or at least the society we mostly read about was much more formal having more rules about proper manners. They would know when and how to greet people. Today we don’t learn those rules of etiquette and therefore don’t know when to say what. We also don’t re-greet people we have seen earlier in the day except with the very informal “hi” or maybe “hello.” I can’t think of once where I remember hearing a second “good ____” from the same person be it morning, afternoon or night.