But I do agree that some people are more about the whole "event" of an apology than the actual results it can provide.
It's usually painfully obvious when someone's doing something simply to make themselves look better or "bigger" than others, and when someone is being honest and transparent as possible.
Anytime someone leads their apology with "Imma be the bigger person and....", they might as well just stop talking to me because that's an insult. I'm the smaller person in this situation? You can't apologize to me by insulting me first.

The foundation of a genuine apology is accountability - and accountability is something that can not only be useful in friendships, but business relationships as well. You should never be too big to admit your fault, own it, make no excuses for it, and keep it moving. Don't wait on an apology from the other person, or a pat on the back for the gesture. You shouldn't expect a cookie for something you should be doing as an adult anyway.