You are missing some things in your logic:

• Users who gain reputation very fast aren't any better than users who gain few up-votes per post and gain access to moderation tools after a few years. Their ongoing contribution brings them their privileges. (I would argue these users are usually the better moderators).
• When people keep posting half-quality posts, they will get down-votes, which will slow down the process.
• Usually, users that aren't really here to contribute won't even bother they 'moderation capabilities'.
• The community as a whole can 'moderate the moderators', which mean usually the effect of a single bad user with some moderation capabilities is negligible.

You are missing some things in your logic:

• Users who gain reputation very fast aren't any better than users who gain few up-votes per post and gain access to moderation tools after a few years. Their ongoing contribution brings them their privileges. (I would argue these users are usually the better moderators).
• When people keep posting half-quality posts, they will get down-votes, which will slow down the process.
• Usually, users that aren't really here to contribute won't even bother they 'moderation capabilities'.
• The community as a whole can 'moderate the moderators', which usually means the effect of a single bad user with some moderation capabilities is negligible.