From time immemorial, prominent placement for accepted answers has been baked into Stack Exchange. The reason is that, by accepting an answer, the OP is saying "I did that and it worked for me; I don't need any more help". That signal is valuable. So we pin that answer to the top of the list, so viewers will see it first. (Except for self-answers, because of concerns over gaming the system.)
There have been lots of meta posts about whether this pinning is actually a good idea when there are other, higher-voted answers. No really, lots. For example:
Let's move some negatively scored answers from the top spot (see links there to several more)
All of this raises what, to me, seems a more basic question that we ought to answer first: what does it actually mean, today, and in practice rather than in theory, when somebody accepts an answer? 'Cause that's the signal that we'd be disrupting if we change how pinning works.
I'm dubious about the theory, in two ways:
On many sites that weren't even a glimmer in Joel's eye when he launched Stack Overflow, answers aren't actually testable or verifiable. I think that sometimes people pick answers that worked for them in some fuzzy way, and other times they pick answers that they like for their own reasons. Subjective-leaning sites can be especially prone to this (as previously noted).
On the parts of the network I frequent, people still answer questions that already have accepted answers. (I had been under the impression that this doesn't much happen on SO, but I was wrong. More on that in a bit.) So the fact that the original asker has been helped might not mean much to the community, which is supposed to address the question for future readers too.
I don't know how to systematically investigate my first point, but we can science the second one. I used this SEDE query (h/t msh210) to answer the question: how often do questions with accepted answers get new answers? (The query reports separately on positively-scored new answers, but this isn't a big difference on most of the sites I tested.) Deleted answers don't count in this query.
I ran the query on the top five sites by number of questions and a smattering of other non-tiny sites. I was surprised by what I found:
Approximately half of the questions with accepted answers got newer answers on: Stack Overflow, Mathematics, Ask Ubuntu, English Language & Usage, Emacs, and Chemistry.
Approximately one-third of the questions with accepted answers got newer answers on: Super User, Server Fault, Programmers, Mi Yodeya, and Skeptics.
I didn't find any in my sample with drastically higher or lower proportions.
That's a lot of answering for questions that the OP said he's done with.
So, to restate the question:
What signal do we intend acceptance to deliver? What are people who see the pinned answer with the green check mark expected to do with that information? How should it modify behavior?
Here's the data I collected:
Site Qs w/accept w/newer A A upvoted
SO 5891756 2860654 2277478
Super User 131019 47618 36618
Server Fault 107697 34887 27483
Mathematics 279096 169396 150686
Ask Ubuntu 70594 35399 27346
English 34726 17995 15557
Programmers 27608 9788 8740
Mi Yodeya 6342 2532 2362
Chemistry 5197 2529 2331
Skeptics 3116 945 871
Emacs 2787 1586 1450