I guess I see things a little differently. When it comes to apologies, they mean nothing to me. I never expect anyone to apologise to me and always wonder why when people do. Saying “sorry” doesn’t change a thing. If someone is sorry, I prefer them to show it with their actions going forward. You’re sorry? Great, don’t tell me; show me. If it’s something trivial, like you step on my foot, and I think it’s an accident, I might briefly be annoyed, but I’ll get over it quickly. I’ll be moving on before the ‘s’ has finished sounding. And if I think you did it on purpose, well then I’ll be in your face and we’ll have a problem. Either way, sorry doesn’t come into it.
EDIT: And yet I still find myself apologising to people. Especially strangers. Maybe it’s a British thing, too damned polite.