I think we can distinguish apologies into two top-level categories: meaningful and meaningless. Meaningless apologies can be further subdivided ("I'm sorry you were offended", or "It's just my culture to be a jerk"), but I'm not interested in that - they're all meaningless.
Meaningful apologies can be easily found via the search engine of your choice, "How to apologize" brings up lots of hits. The thing they all have in common though is an acknowledgement (in one form or another) that the person apologizing was legitimately in the wrong, and that they will endeavor to not do that again.
It's that last bit that is important. It's not sufficient for a company to apologize for dumping oil in the ocean or a person apologize for using a racist term. A real apology acknowledges harm caused, and shows how the entity apologizing will rectify past harm and prevent future harm.
This is why, in my opinion, at least, so few apologies legitimately improve anyone's standing. It's not that "cancel culture needs heads", it's just that people expect to say, "I'm sowwy", rub their toes in the dirt, and be let off the hook without doing anything to really undo the harm caused. People rarely even acknowledge the harm they cause, let alone do anything about it, in these so-called apologies.
So no: people who demand apologies don't just reject them after they're given. It's just that most of the time, the apology is meaningless.
One of the explicit design choices in this was to limit people's tendency to screw up apologies in the heated moments when they haven't yet internalized the outside world's perspective of their message. I'm glad you brought up the searching of how to apologize - it's one of those super important life skills that we haven't done a good job of teaching people about. We have to design with this constraint in mind.
One of the things I think about most in design, especially in design of social products, is limiting self-sabotage. This is because there's really significant emotional risk in social systems of feelings like being exposed, misunderstood, etc.
This is why I favored the approach of not including a Follow-up or further explanations. It makes the choice Mea Culpa very simple, favoring cooling off of conflict over continued debate. Basically people can go back in their corners and think about things, and figure out how to approach things again later if they choose. It is an intentional choice to favor respectful debate over maximal information exchange, acknowledging the medium's tendency to escalate conflict and the presence of many bad faith actors.
Also note this feature does not take the place of the apologies you're talking about, it just offers an acknowledgment of mistake and an opportunity to forgive.
The awareness of the user's emotional state leading to the possibility of self-sabotage is a brilliant aspect of this design. I just wanted to say how much I appreciate that line of thinking in this context. It's lovely to see consideration of the user's emotions modelled as a practice that should be more common, as, after all, social media is a form of computer-mediated human interaction and all human interaction leads to emotions.
Yes, I agree with your overall thesis. A feature like this can help normalize people publicly admitting that they made a mistake, and walking back that original Bad Tweet (or whatever).
Meaningful apologies can be easily found via the search engine of your choice, "How to apologize" brings up lots of hits. The thing they all have in common though is an acknowledgement (in one form or another) that the person apologizing was legitimately in the wrong, and that they will endeavor to not do that again.
It's that last bit that is important. It's not sufficient for a company to apologize for dumping oil in the ocean or a person apologize for using a racist term. A real apology acknowledges harm caused, and shows how the entity apologizing will rectify past harm and prevent future harm.
This is why, in my opinion, at least, so few apologies legitimately improve anyone's standing. It's not that "cancel culture needs heads", it's just that people expect to say, "I'm sowwy", rub their toes in the dirt, and be let off the hook without doing anything to really undo the harm caused. People rarely even acknowledge the harm they cause, let alone do anything about it, in these so-called apologies.
So no: people who demand apologies don't just reject them after they're given. It's just that most of the time, the apology is meaningless.