Concerning the continental european situation:
Addressing an officer in the polite plural can be understood as addressing the office, implying that the actions of the officer are expected to be in accord with their responsibilities, and mostly free of personal value judgement. Consequently, there is--in German or French at least--the same honorific used for actual plural addressees, and the honorific appears impersonal and thus potentially impolite in personally intimate conduct, and offering the 2nd p. sg. between e.g. collegues is honorific in itself.
That describes only a subset of the usage, though.
The primary distinction is made only after kindergarden, in primary school, where teachers are addressed in the plural 3rd p., but the individual pupil is addressed regularly in the singular 2nd p. and the whole of the class is addressed regularly in the 2nd p. pl. It is thinkable that this stems from teacher positions in grammar schools being taken by officers, but this does not matter in a synchronic analysis. Especially children still learning the language may simply take the contrast for granted.
The diachronic analysis might have a long historic tail and vary by language, culture and domain. In many domains the direct address to an authority is taboo-ized, arguably so if imperative forms would start with the nominal. In this sense, the idea of distance as mentioned by @MarkBeadles is often a very real physical distance, that is so ingrained that it prevails after approaching closer. To conclude, note that even the 3rd p. sg. has been used as form of respect (and consequently in sarcastic disrespect).