What you're asking for is not always possible. In SQL Server, for example, what used to be "the best way" to do something may have been replaced with a better solution in newer versions of SQL Server. As such, the "best" answer today may not coincide with the oldest and/or most up-voted answer. In fact I often see a question being closed as a duplicate of a much older question - yet when I visit the original question the answer is no longer the best answer. Just because the question is the same and there is an accepted answer does not automatically mean that the answer is still a good answer. I'm sure this happens in a variety of other non-stagnant technologies too.
Sadly the only way to improve that scenario would be to have a "best answer" per version, or to consolidate all of the best answers, neither of which are made very easy with the software and the prevailing opinions on the site.
I agree in general with your sentiment, but the difficulty I see is that for some technologies it makes no sense at all, even though for others it is perfectly logical. I don't think there is going to be a flawless way to improve the duplicate finding algorithm across all technologies. For some the highest voted will make sense, but for others it will just lead to quicker inappropriate closing of questions that really have a better answer today than their duplicates provide.
In the end I think that in most cases it will continue to be up to us as close voters to select the duplicate with the best answer. I suspect that even without the example I list above the best answer won't always be the oldest or the one with the most votes.