What you say is accurate, but I think the benefits of saying sorry are much bigger than what's being mentioned here.
I find that when I say sorry on a frequent basis (and I make mistakes every single day), it inspires courage. I'm not afraid of being wrong, because I can trust myself to correct my mistakes. Because I know I'll make mistakes and can correct them, I can steam ahead and crash into walls and have the resiliency to get up very fast.
I'm also not very worried about hurting people, because many times after I've hurt them and say sorry, the relationship to that person is actually improved. In other words, it's better to hurt them, acknowledge the mistake and fix it, then not taking any action at all.
Saying sorry has so many benefits. Another is that the internal fear of being "discovered" goes away. "What if someone finds out" becomes a though of the past, and instead there comes the pride of "yes, I did this, and I stand by it, because I've corrected my mistake".
So I'd say; make heaps of mistakes, learn from it, apologize, and go full throttle. Life is short, make the most of it. You cannot drive a formula 1 car with a lot of weights hanging behind it. Fix errors and move on.