Your analysis is fundamentally flawed because it is completely based on observation bias. You see questions where the highest-scoring answer is better than the accepted answer and conclude that this should be done all the time.
If the accepted answer wasn't shown at the top, there would be a feature request for it to be shown at the top, to allow the asker to convey that no matter how much the community loved one answer, this other answer is the one that actually works.
Supposing that there is one answer which is objectively best, there are several categories of threads:
- The best answer the highest-scoring one and is accepted.
- The best answer is neither the highest-scoring one nor the accepted one.
- The best answer is the highest-scoring one but not accepted.
- The best answer is accepted but is not the highest-scoring one.
In case (1), there is nothing to change. In case (2), there is nothing to do unless you have a different way of recognizing the best answer. So the question is which of (3) and (4) should be given preponderance.
To decide which one of (3) and (4) to favor, one factor is which one happens the most often. Yours isn't the first request to favor (3), but so far I haven't seen anyone put forward evidence that (3) happens more often by (4).
Unless the frequency argument strongly favors (3), there is another reason to prefer (4). The highest-scoring answer is guaranteed to come out second at worst. On the other hand, if the asker determines that a different answer is better, then the only way they have to make it be more visible is to accept it: otherwise this answer may be buried anywhere in the list.
This is especially useful when a new answer comes along a long time after the question was posted. By accepting the new answer, the asker can convey the message that this new answer is better, more up-to-date, etc. — this is a lot more useful than a comment below the highest-scoring answer, especially if that answer already has a lot of other comments.
Yes, sure, I've seen plenty of questions where the asker has accepted an early bad answer and a better answer outscores it. But askers who do that tend to ask mediocre questions that aren't very useful anyway. There is a strong corellation between askers who maintain their questions — including accepting new answers when they're better than what was there before — and askers who ask widely useful questions.
Thus putting the accepted answer on top has many advantages:
- It provides an opportunity that is completely missing from the opposite choice.
- It has a better chance of being the right thing on useful questions.
- It doesn't do much harm: at most the highest-scoring answer will come second; and if the accepted answer has a negative score, this is a sign to readers to take it with caution.
For these reasons, I am strongly against moving the accepted answer away from the top¹ (no matter what its score is), unless it is demonstrated that there is a significant majority of cases where this is the superior choice.
I'd be more in favor of allowing some way to have a third party accept answers on abandoned questions, which should handle most cases of accept-the-first-answer-and-move-on. I don't know what form this would take. In any case, if a thread is really bad, there's always the option of closing it as a duplicate of a thread with better answer.
¹ Excepting self-accepted answers, where there is no independent review at all, unlike non-self-accepted answers which involves two distinct users.