Audit log is not very useful

The audit log only shows a summary of what has been done.  In particular it does not show the contents of removed messages, and messages removed by their author are not logged at all.  This means that users could harass others and then remove the offending messages before moderators notice, leaving no evidence of the harassment.  It's unreasonable to assume that every server has moderators watching the discussion 24/7.

Messages removed by moderators at least get the removal event itself logged, but the contents are lost.  Thus it's not possible for others to judge the moderation choice after the fact.

With the manage channels permission one can even disappear entire channels of evidence at once, but I guess this boils down to trusting your moderators.