Although I don't really like the proposed idea (moderators changing accepted answers), I do like the sentiment behind it. As Andrew has nicely spelled it out, this seems to be an issue of balance between the short-term goal of “I want an answer to my question, now!” (and acceptance of an answer means fulfillment of this goal), and the long-term goal of keeping a database of usable answers for people later searching-for/stumbling-with a page.
It seems that most people around think that the short-term goal is all that we should care, and the long-term goal is simply a “nice” by-product. However I'm one of the few who disagree.
At least for me, trying to build a mostly correct and up-to-date source of answers for (La)TeX questions is one of the reasons that got me motivated to participate and spend some of my time in this site. The web is already full with incorrect and outdated information about (La)TeX which is only kept alive because people searching for solutions on the web keep stumbling with the old and obsolete answers. From the beginning I thought that this site could finally be a solution to this problem, and that's why (for example) I tend to be more keen on heavily editing answers “for the future”.
I'm not suggesting, of course, that we should have to police around the site and have this long-term goal in mind all the time. Perhaps I would consider checking from time to time the most voted/viewed questions for sanity. But the ideal would be that we don't have to do much more for the site to be able to fulfill the long-term goal as well as the short-term one; and so, for the particular issue raised by the OP, this is my suggestion:
How about requesting a feature where the most-voted answer (perhaps after a certain threshold of votes) gets to be shown before the accepted answer?