Based on reputation earned, SE sites give different types of privileges to users.
I am only talking about moderation privileges, which have some serious impacts on the community. For example (editing, close and reopen votes, access to moderation privileges).
The privilege will also be lost if the rep goes below the required limit.
I have seen many users, mainly on Stack Overflow, that have just created an account less than 10-20 days and already have reputation of more than 1000 earned from bounties.
A person, with 9 days on the site, earned almost 850 and another one, from 23, earned 1.8k.
In such a case, within a week, they may get the privilege to approve suggested edits and also edit inline.
Within some more days, they will be able to cast close and reopen votes.
As said, they are noobs in SE and they may mot have an exact idea of how the community works.
To make it clear, assume that a person earned 2k rep in 10 days from bounties, he can edit inline. But he may not aware of when a post should be edited.
There may be chances of misusing the privileges. It is not their fault but they may not aware of the flow of community from experience.
Also there may be chances of people editing other's posts to abuse (It has already happened on SO many times).
Along with reputation, have some other criteria in order to gain a privilege.
Edit Questions And Answers - 2000 rep and should have at least 100 approved suggested edits.
Cast Close And Reopen Votes - 3000 rep and should have at least 100 helpful flags.
Access To Moderator Tools - 10000 rep and should complete 1000 review tasks in at least one review queue.
This happens only in rare cases. But I found people with 4k rep in 40 days too.
So, giving such privileges to Rep Hunters is not a good idea because there may be chances of misusing the privilege.
One more feature request - Trusted user privilege should be obtained only if they have a Marshal, Copy editor and at least 2 steward badges.
Marshal - raise 500 helpful flags.
Copy Editor - Edit 500 posts
Steward - complete at least 1000 review items in one review queue.
As a side request, don't apply this on beta as well as small sites.
Please implement it in SO as an experimental/beta feature to see the result.