Is the word "sorry" not a little bit like the sentence "I love you"?
We say it over and over, and we mostly don't mean it really. I only say "I'm sorry" or "I love you" when I really mean it.
To me, the word "sorry" is only well if something happened that was your fault. Like saying "I'm sorry that your mother died" is kind of unlogical since you have no part in her dead. Also using that when you arrive too late at your job, because of the late train, is also nonsense to me. You can't help it, and for that you can't be sorry. At least, that is IMHO.
I'm only sorry when I hurt someone and I regret it later. But I guess that's it.
The proper thing to say after you said sorry (after stepping on someone toes), is to ask if you can do anything to make it up again.