It is not our job, as a community, to police for copyright violations. We are not the owners of the copyright, thus we don't know how an image is "allowed" to be used.
There was a Meta.SE post about how users should enforce NDAs. This is similar.
First, Stack Exchange, Inc (hereafter SEI), is not party to such agreements. Second, making any effort to enforce third party agreements may put SEI in a position of being liable for NDA violations it misses.
The same logic applies here. If we do start attempting to enforce this, even as a show of good faith, when we inevitably miss something Stack Exchange may be liable.
A similar question was asked on Math.SE as well. An answer by another moderator starts with this:
SE has told us about copyright is that it is not our job as moderators to enforce it. Copyright can be rather complicated and I don't know enough about it to correctly deal with it. So copyright stuff is something that we leave entirely to SE (plagiarism is different, we enforce our own rules there, which is different from copyright law).
The guidelines for anyone that wants to remove a post that violates their copyright has to file a DMCA takedown notice and SE executes them. One important point here is that SE has absolutely no room for judgement here, they have to blindly execute the takedown notices to qualify for the "safe harbor" part of the DMCA. So bringing in a local mod makes no sense if there is no room for any informed decision anyway.
If someone wishes to protest the posting of an image due to copyright reasons, there are legal actions they can take. They can file a DMCA complaint to Stack Exchange. Stack Exchange will then deal with the post as appropriate.
We, as a community, should strive to post content we are entitled to post.
It is also important to remember that Stack Exchange is a U.S. company. As such, there are Fair Use arguments that can be made for single images. This doesn't prevent a DMCA take down from occurring, but it does provide one avenue of justification for using images under copyright.
Important points about Fair Use, from the US Copyright Office:
(1) Purpose and character of the use, including whether the use is of a commercial nature or is for nonprofit educational purposes:
Courts look at how the party claiming fair use is using the
copyrighted work, and are more likely to find that nonprofit
educational and noncommercial uses are fair. This does not mean,
however, that all nonprofit education and noncommercial uses are fair
and all commercial uses are not fair; instead, courts will balance the
purpose and character of the use against the other factors below.
Additionally, “transformative” uses are more likely to be considered
fair. Transformative uses are those that add something new, with a
further purpose or different character, and do not substitute for the
original use of the work.
(2) Nature of the copyrighted work: This factor analyzes the degree to which the work that was used relates to copyright’s purpose
of encouraging creative expression. Thus, using a more creative or
imaginative work (such as a novel, movie, or song) is less likely to
support a claim of a fair use than using a factual work (such as a
technical article or news item). In addition, use of an unpublished
work is less likely to be considered fair.
(3) Amount and substantiality of the portion used in relation to the copyrighted work as a whole: Under this factor, courts look at
both the quantity and quality of the copyrighted material that was
used. If the use includes a large portion of the copyrighted work,
fair use is less likely to be found; if the use employs only a small
amount of copyrighted material, fair use is more likely. That said,
some courts have found use of an entire work to be fair under certain
circumstances. And in other contexts, using even a small amount of a
copyrighted work was determined not to be fair because the selection
was an important part—or the “heart”—of the work.
(4) Effect of the use upon the potential market for or value of the copyrighted work: Here, courts review whether, and to what
extent, the unlicensed use harms the existing or future market for the
copyright owner’s original work. In assessing this factor, courts
consider whether the use is hurting the current market for the
original work (for example, by displacing sales of the original)
and/or whether the use could cause substantial harm if it were to
become widespread.
