> None of these necessarily imply the speaker has actually done something wrong

You’d be surprised. The culture of kidzukai has two core tenets: (1) You must anticipate and cater to the other person’s every need and whim. If you fail you must apologize. (2) You must not allow the other person to do (1) for you instead of you doing it for them. If you fail you must apologize.

This means that every interaction between people who are even slightly close to each other in the social hierarchy is 3D chess which always ends in one or both of you apologizing to the other.

p.s. Gomen kudasai is “please permit me” to enter your house, not really an apology like gomen nasai.