To clarify: My point was that the crucial aspect is not that people observe a punishment, and then infer that they should not commit crimes later. Rather, the important thing is that people, to the extent that they correctly model the rest of society and its response to their crimes, get an "internal simulation" that outputs "they will inflict disutility on you even if it's expensive to do so, and even knowing that it failed to deter you". And this model can only be correct and have this character if people really do punish in the crime-instances.

In other words, to the extent that people require punishments to deter, they only require subjunctive, not causal deterrence -- though obviously the latter is factored in.

The second half of the answer is that most people believe in justice.

That's what I was referring to as the "otherwise-ungrounded deservedness of others [who defect] of being treated badly" -- this internalization of subjunctive (and acausal) criteria feels like a desire for "justice" or "what is right" on the inside. In other words, we have causal reasons for doing things, and separate from that, we have acausal criteria that often conflict, and when the acausals outweigh, we get the feeling of, "this person should be punished, even if expensive, and even though the crime has already happened".

That is generally called the "sense of justice".