why do wish someone good morning/evening or night?

I'm not sure we say this because we truly care, although in some cases we do. We say good morning/night because it's like a greeting or a farewell...kind of like how we say hello and goodbye. To me, it's just being friendly because I've definitely said good morning/night to people I didn't particularly like. But each person can have their own meanings for these words. Some may see it as caring for the other person or simply as a greeting or goodbye

I do not think that we use this phrase with any feeling. This is used just as a greeting but is very effective in mood lifting even if speak it without any concern.

I often use it as a social convention. It is a way to end a conversation without being rude. Yes, I also wish it sincerely to people I know well and who are my friends. We should care for our friends and our family. I do not quite care as much for the person taking my money at the store, but I do wish them well, with "Good morning" or "Good night" or "have a nice day." I doubt that I would ever wish someone a bad night or evening or day. I wish most people well.