Post notices aren't fully developed.
Originally annotations were a response to the practice of adding "citation needed" headers on Skeptics. Rather than encouraging anyone with edit privileges to add canker sores, they are official, moderator-approved banners. But nearly all the problems of the unofficial headers still exist with post notices. In particular:
They are often used in place of comments, downvoting, alternative answers, and/or deletion.
While some of the notices threaten deletion, they often stay in place for years. It's a toothless warning and an eyesore.
Unless you know how to get the timeline view or dig the information out of the PostHistory table, users don't know who added the notice and therefore have no way to communicate with them. That's especially frustrating for new users since they are sent a notice in their global inbox with no guidance on how to get the notice removed after an edit.
Two of the post notices are tuned for Skeptics. The third non-system notice, insufficient explanation, only makes sense for answers. There's no way to customize the notice to fit a particular situation, so we occasionally see them misapplied.
The community has no oversight when post notices are added or removed. I assume this isn't a major problem at the moment since moderators are typically reliable. But who knows?
Insufficient explanation could be answers' answer to "on hold".
A pattern we've seen across a number of sites are somewhat rare answers that get heavily upvoted despite obvious problems. On Skeptics, these posts are called pseudo-answers. On technical sites, the problem might manifest in answers to solve the OP's immediate problem, but might cause problems if naively applied. Religious sites sometimes get answers that are popular and perhaps even correct, but lack evidence that typify useful answers. The common thread is that the answer does not explain itself as well as the community would like.
Downvoting and alternate answers, usually the best solutions to not-so-useful answers, are unsatisfying when a post already has a ton of upvotes. Deletion tends to be more satisfying, but it's often hard to arrive at consensus when it comes to deletion and moderators can be reluctant to delete unilaterally. A similar problem has more or less been solved for questions by the on hold -> closed process.
How post notices might get fixed.
Many of the problems with post notices seem fixable. For instance, pseudo-answers might get an improving edit with judicious use of a post notice. The workflow I imagine is:
A user with the post notice privilege discovers a problem with an answer and applies the insufficient explanation notice. The user's display name and the date would be included in the notice. They would also be pingable in the comments.
After an edit or a sufficient length of time (a week?), the answer is sent to a specialized review queue.
Reviewers can chose to remove the notice or delete the post. The number of votes needed would be site configurable to allow for different answer cultures.
As a result, post notices set answers on the path toward deletion and there's a real incentive to fix the underlying problem. Notices don't have a chance to hang around long; answers need to be deleted or the post notice removed in order to clear review. Nobody (with the possible exception of moderators) can singlehandedly add a post notice thereby ensuring oversight.