That's a fundamental tension in the purpose of the site. If the particular problem of the asker is the end goal, then duplicates would not be closed. All other site criteria institute a strong demand for general interest of questions.
Part of its success may be deftly balancing those two conflicting interests. On one hand is the role of helping people, and the other hand is a non-repeating and immediately useful knowledge base. Both of these demands bring human attention, and satisfying either requires real work by a human. The challenge is to keep the relevant human around just long enough to do enough work so that you have plausibly usable content.
Accepted answers are a site design tailored for one use, but it is fantasy to pretend that it harmoniously exists along side the other use. They are not separated. Design elements oriented toward one way of use degrades the other use.
But practically forcing users to select an answer as "good" should probably not be the only way to do this.
I know because I write those kinds of answers.
I wish they would unpin those answers from the top - leave the green checkmark, just let me sort by whatever has the most votes recently - say in the past year. Then we'd get more up-to-date answers more attention, and more readers would find them.
In the common case, the accepted and best answers will probably be the same, so keep the classic green checkmark there.
When the accepted and best answers don't match, have two checkmarks (or whatever) - one that explicitly says "user XXX accepted this answer" and the other that says "this is the best answer".