As part of being a 10K+ user, you get access to tools that are very closely related to the tools that a diamond moderator sees.
Flags and suggested edits, while different, both involve pending actions that are not completed until someone with some level of authority, like a 2k+ user or a 10K+ user, can approve them.
To elaborate, these edits are held back visually from all other users until approved, so the quicker they're reviewed, the faster the edits are applied.
The other review queues, while important, involve actions that suppress posts rather than expose them. For instance, first posts and late answers, if not reviewed, are still visible to all users. These posts need reviews only to receive more upvotes or to receive special attention if they're poor quality, like editing or deletion.
For close votes and delete votes, the goal is also to suppress or remove poor quality content. There's not as big of a rush here. Again, with edits, the goal is to expose content.
Keep in mind that users with less than 10K+ rep can still approve suggested edits, but they don't see the moderation tools that you do, and they don't see the bat signals. While these things may be legacy tools that existed before the new review tools were released, the old review queues also weren't highlighted via the bat signal, only suggested edits and flags.
Lastly, an important point raised by kiamlaluno is that the suggested edit queue is finite. If people aren't approving edits and they max out the queue, then no more suggested edits can be made.