Has anyone ever done something so horrible to you that "I'm sorry" couldn't fix it?
"I'm sorry" never fixes it; "I'm sorry" is a weasel's attempt to get out of responsibility by placing guilt on the one who was injured.
What does fix a transgression? Take a lesson from the Catholics - add works to atone for the sin [1], not just words. And go forth and sin no more.
So when you've done something horrible to someone, don't say "I'm sorry". Apologize by fixing the window that you broke, or telling folks that you were the one in the wrong, or by doing something else that corrects the mistake that you made. And then you can say "I'm sorry" and the person will know that you mean it.
Until then, "I'm sorry" is like the garden that Ben Franklin described.
John
[1] That's what these are - social sins. And "I'm sorry" is an attempt to magically use patter to atone.