It just happened to me a few minutes ago.
I had submitted a question to EL&U for which I only reluctantly accepted an answer weeks ago. Only to find out today that somebody else had come up with a nearly perfect answer.
Of course I shifted the green tick to the better answer, but I also felt that that was a small reward for the effort of digging up the question from the bottom of the stack and providing an enlightening answer.
May be the condition could be that the question's originally accepted answer must have been accepted more than NN days before the shift in order to avoid people fiddling with the conditions. That would add some viscosity to the system. There should be a numerical threshold anyway.
As I was answering Gilles comment, it also occurred to me that a badge to earn would have the positive side effect that people would be more willing to browse through older questions to see if they have a genuinely better answer to propose.
Overall this would
- Unearth old questions => less duplicates.
- Increase the quality of the pool of answers for existing questions because a good answer to a tricky question ultimately depends on whether a person knowing the answer comes in contact with the question.
- Improve the quality of the site because accepted answers would have more chance to have been reviewed even once accepted.