Accepted answers are useful to show which answer helped the OP the most and are likely to be helpful to others; therefore they show at the very top of the list of answers; irrespective of the sort order or the votes on the accepted answer. This is usually has a good effect; showing the OP's favourite answer followed by the communities most upvoted answer (probably two very good answers) at the top.
However this can have a slightly strange effect when the community is highly against the accepted answer and downvotes it heavily. In addition to having a (strongly believed to be) wrong answer first it also turns grey; leading to an odd visual effect of something that looks like the top answer being difficult to read and looking like a footnote.
For example all of these, they're wrong, everyone knows they're wrong and yet they sit at the very top of each of their questions. Their authors can't even correct the situation because accepted answers can't be deleted.
Ultimately the sort order isn't for any political reasons; it is to show you what is likely to be helpful first. The accepted checkmark is a strong indication that an answer will be useful, on the other hand a negative score is an indication that an answer is unhelpful; at some point the downvotes should win.
When an accepted answer is sufficiently downvoted to turn grey ( <=-3 ) then it loses its accepted answer privileges to be at the top of the answers list as the community is clearly strongly against it. This avoids the mixed message of putting it at the top (saying its important) and marking it grey (saying its unimportant).
What I’m not proposing
I'm not proposing removing its check mark or in any way undoing its accepted answer status, it was accepted by the OP and we shouldn't mess with that.
Don't put heavily downvoted accepted answers at the top has a similar thrust but seems to be saying that an answer with downvotes, even if it has an overall positive score should not be at the top; that seems slightly mad and I'm not proposing that.