That's absolutely laughable. Why would people accept apologies they think are insincere? And how would that possibly lead to "a better world," except for people who spout nonsense then pretend they're sorry later?
But that's frequently enough incorrect. Setting up a "virtual truce" where we all forgive quick apologies leaves us a little happier IMHO. Yeah we might be a tiny bit naive for this, and some bank robbers might slip through the cracks, but a less anap-judgy world is a nicer place to be overall (at least from my experience).
Societal engine lubricant. There is too little time for every squabble to matter.
I don't care about winning or losing. But I don't know how to say, "whatever, moving on" in a way that itself doesn't get interpreted as further pettiness.
People change. And Adams is now certifiably insane.
I struggled with this for years. In the end I just settled on saying "Respectfully, I think we will need to just agree to disagree. No hard feelings." A few times I've had to drop the "This conversation is going nowhere good. Let's talk about something else."
Being direct is under-rated. I find people aren't offended when you do it, as long as you are maintaining some basic amount of social decorum / grace.