The fact that moderators cannot flaunt their position of authority is embedded in the PW philosophy. Moderators are here to keep things in check, not to be dictators.
From your teachers example: you will observe that when the behavior of students is controlled in this way they tend to be extremely rowdy any chance they get while the teacher is absent. In contrast if you look at a university environment, teachers call themselves facilitators, and try to come (in some cases they even are) on a similar level as the students. Where learning is the main purpose, not a hierarchy of authority (which we as a nation just love). That is the motto here at PW also.
Plus there are two more reasons.
- We already have people pointing out mods by their names (even when they aren't titled as one) and developing personal grudges for some moderating actions they would have done
- Moderators, in almost all cases, are regular members who were entrusted with the responsibility because they behaved a certain way around the forums. And all mods I know would want to be able to regularly participate in forums - which would not be possible if they have a badge under their names
if only all members would behave well, we wouldn't need moderating actions - just forum management 
and all this talk of show of authority would not even be needed.
