Sure, it wouldn't always be effective. But things that--when described linguistically to you--sound obvious can be subtle enough when they actually happen to others that they work anyway. Actually believing that you have acted imperfectly and can do better next time and conveying this in apology form makes it less obvious. And in fact, if you are trained to apologise for little things in the face of big things even without an audience, then your outward conduct may even be mostly indistinguishable between the two cases anyway.