Has what worked in the past? Admitting you were wrong and apologizing? Sure it's a good way of resolving conflicts if you were actually wrong. People grow and change throughout life, I don't think that being a knucklehead in the past necessarily means you're a knucklehead now.
Admitting you were wrong and apologizing in public, specifically.
An individual can be reasoned with, placated. You can make reparations, promises that the other person will believe because of a precedent of mutual trust and forgiveness.
The angry mob is irrelevant. There are more individuals watching quietly than people making their positions public. The mob will chill when their friends ask them to post-apology. I have been on all sides of this phenomenon: the chiller, the chillee, the apology. It works.
The mob is big enough that they are not necessarily even friends with each other. People who ask the mob to chill risk being mobbed in turn. Punishment of non-punishers is how mobs sustain themselves.
The angry mob is the reason people like James Damore get fired while his openly white-male-hating coworkers are free to post their opinions on Twitter with no consequences at all. They are not at all irrelevant.
