Stack Overflow was the first SE site, and many mechanisms were designed for SO and not necessarily for all the different sites that came after it. The "accepted answer" concept is one of those mechanisms that exists pretty much unchanged for years now.
On a site about problem solving, which SO is, the concept makes sense. The asker gets a few answers, tries them out and accepts an answer that worked for him. When you're dealing with a programming problem, the asker can in almost all cases verify if the answer worked for them, in many cases you can just copy the code, run it and check the result.
The situation changes dramatically on sites that are not really about problem-solving. I'll use two sites I'm familiar with as examples, but there are probably more. Skeptics and the new Health site are sites where many questions are asked by users that do not necessarily have knowledge needed to evaluate which answer is better. On Skeptics there is the additional problem that for some controversial subjects, users tend to accept the answer that fits better to their own world view, not the better answer overall. This leads to worse answers being shown first, instead of the highly upvoted but not accepted answers.
Having an accepted answer doesn't really provide any value on such sites, the askers don't have an easy way of verifying answers in most cases. Voting alone should put the best answer at the top, and letting the asker determine the sorting order can be problematic.
The accepted answer concept has too much effect on reputation gain for it to be removed entirely without causing a lot of issues. But the changed sorting order for accepted answers is something that could be changed without significant side-effects. I know this has been declined before, but I think the situation for some sites that differ fundamentally from SO is different enough to warrant revisiting the decision. The solution might be something like a per-site toggle, or a global change. I'd prefer changing this globally to minimize confusion, but there are certainly other options possible.