That’s a #3 colloquial definition which is a perversion from the literal meaning and further testament that moderators are misnomers.
The #1 definition is:
noun
a person or thing that moderates.
The definition of moderate is:
adjective
kept or keeping within reasonable or proper limits; not extreme, excessive, or intense.
verb (used with object)
to reduce the excessiveness of; make less violent, severe, intense, or rigorous.
verb (used without object)
to become less violent, severe, intense, or rigorous.
noun
a person who is moderate in opinion or opposed to extreme views and actions, especially in politics or religion.
So a moderator is someone who or something that is not extreme/excessive/intense and practices the action of reducing excessiveness/intensity of something.
Any other definition is a perversion from the literal meaning.
The British dictionary suggests a moderator is more likely to be a church minister or heavy water in nuclear reactors than a policeman of message boards.
British Dictionary definitions for moderator
moderator
noun
- a person or thing that moderates
- Presbyterian Church a minister appointed to preside over a Church court, synod, or general assembly
- a presiding officer at a public or legislative assembly
- a material, such as heavy water or graphite, used for slowing down neutrons in the cores of nuclear reactors so that they have more chance of inducing nuclear fission
- an examiner at Oxford or Cambridge Universities in first public examinations
- (in Britain and New Zealand) one who is responsible for consistency of standards in the grading of some educational assessments
- a person who monitors the conversations in an on-line chatroom for bad language, inappropriate content, etc
The #7 definition above is a cop
cop
[kop]
noun Informal.
- a police officer.
- a person who seeks to regulate a specified behavior, activity, practice, etc.
police
[puh-lees]
noun
- an organized civil force for maintaining order, preventing and detecting crime, and enforcing the laws.
- (used with a plural verb) members of such a force.
- the regulation and control of a community, especially for the maintenance of public order, safety, health, morals, etc.
- the department of the government concerned with this, especially with the maintenance of order.
- any body of people officially maintained or employed to keep order, enforce regulations, etc.
- people who seek to regulate a specified activity, practice, etc.
The difference between a cop and a moderator is the latter is only interested in the intensity and not the topic; the topic is irrelevant: his only job is to bring things back to center. However, a cop has no regard for intensity since his job is to blindly and mechanistically enforce prescribed rules.
So if moderators are to be cops, then they should be called cops. If they are to be called moderators, then they should be moderate and practice moderation. Otherwise it’s like pro-lifers in support of the death penalty; they shouldn’t be called pro-life if they are not.