There seems to be a social convention that an apology has to be accepted and that someone who does not is unfriendly and a bad person. This seems strange to me, because an apology often tries to undo deeds with words, or cancel unthinking words with considered ones.
The willingness of most people to trade words for deeds seems irrational to me – there is a qualitative difference between words and deeds, in that words can be neutralized within the hearer’s mind. If the hearer or reader does not understand, hear or attach emotional significance to words, then these have no effect. Deeds, on the other hand, have consequences that are not just in people’s heads. A punch causes bruising even if imagined to be a caress. An insult does not cause bad feelings if it is interpreted as a joke by all concerned.
Accepting words in compensation for deeds makes one manipulable. The perpetrator of bad actions can get away with them repeatedly by promising each time to change and to sin no more (Hitler’s “last territorial demand”). The social convention that words have to be accepted as compensation helps the unscrupulous. If instead good works in sufficient quantity were required to make up for misdeeds, then taking advantage of others would be less profitable. Some people would have to spend a lifetime undoing their crimes, which creates the incentive problem of how to make criminals work. Perhaps gradually easing ostracism and restrictions as the debt is worked off. The quantity of good actions required must be large enough to make the overall profit from a bad deed negative.
Cancelling unthinking words with a considered apology benefits impulsive liars who initially insult and then talk their way out of the opprobrium by pretending to be sorry. Every time I find in the media that a politician or a white collar criminal says sorry, I interpret it as them being sorry they were caught. If they were sorry about the deed itself, they wouldn’t have done it in the first place.
A good person who did something bad by accident would volunteer to make amends. They would not have to be forced to it as punishment. Of course, if volunteering to compensate starts being interpreted favourably enough by society, then selfish and manipulative people would also volunteer. Making amends is a costly signal of good intentions, but if the benefit of signalling is large enough, then even the bad types signal to imitate the good.