The idea of an "Accepted" answer that can only be awarded by the asker makes a lot of sense on Stack Overflow and other sites where people are trying to solve an immediate problem. There are many technical reasons that a person might not be able to use the top-voted answer, so it's helpful to have a way of privileging a less popular answer that works for their specific situation. It's a win-win because the asker can signal the answer that actually solved their problem and the community can signal the answer that is generally seen as "best". (Often it's the same answer, which is convenient.)
But I've noticed that some sites don't work that way. On a site like History.SE, the asker might be the worst person to pick a canonical answer. Or at least, there's nothing special about the asker since they don't have any unique problems that need to be solved in an answer. In a sense, the asker of a History question is not asking for themselves or their own circumstances, but for anyone who will use Google to search for answers. When Joe Googler discovers that an answer has been accepted by History.SE (we can't expect him to know that accepted answers are chosen by the asker alone), he will naturally assume that the answer has been given some sort of stamp of approval. That can be a mistaken assumption.
I've floated proposals on other sites that have the same profile. My plan is to develop a consensus across a number of sites in order to propose something on Meta.StackExchange.com. A comment on an answer to one of my questions here, spurred me to bring this up here. Obviously, I'm not really active here (yet?), but I get the sense that Accepted answers might be a stumbling block for users not intimately familiar with Stack Overflow. Feel free to vote up or down this question to indicate whether or not you feel this change would help your community. And also, feel free to answer with alternative proposals for consideration.
Answers that have been "Accepted" by the asker are no longer pinned to the top of the answer queue. All other effects of accepting an answer will remain the same on History.SE, but the accepted answer will be sorted just like any other answer.