I don't think logs are needed in community moderated by single person, don't need logs to know who did what.

But for something like Reddit when there is more mods the anonymity basically means impunity to any judgement; nobody but mods themselves can say whether a certain bias in actions can be attributed to few mods or to everyone in the mod team.

And frankly if you can't handle a critique of your actions you shouldn't be moderating actions of others in the first place