Well, we do really. Community members get more privileges the more reputation they earn, and at 10,000 reputation it opens up access to the Moderator Tools. this gives you access to viewing deleted posts and vote for deletion, among other privileges. It also grants access to the moderator tools themselves, so you can view lots of different reports about what is happening with posts, viewing history of recently deleted posts, bounties etc.
At 20,000 reputation you get access to even more tools and the ability to undelete posts as well as other options.
StackExchange refer to such community members as '10k Moderators' whereas each site get a few dedicated 'diamond moderators' (such as myself). We get access to more tools, but those more relate to handling users rather than handling posts (disciplining users, sending messages to specific users, merging accounts etc) but those require more responsibility as we have access to information about users that is not available to the general public. Opening such information up to just anyone with a high rep wouldn't really be ethical, and would be a breach of privacy, as we have been elected and approved by the general Stack Exchange management and comms team to be granted access to such information.
As such, diamond moderators are only appointed when deemed necessary for the community, and are elected by the users so that regular users don't have to worry about just anyone with high rep having access to information unavailable to the public.