I keep seeing this kind of question come up on meta, and this keeps getting marked as a duplicate. However, the answers in the referred questions are always about how the new user doesn't HAVE to accept an answer.
I think this isn't actually addressing the problem, and I'd like more thoughts on the following, which I posted as a late answer to this question, which was immediately downvoted and subsequently somewhat buried without much comment(the question, not the answer):
I don't think new users are intentionally not picking a best answer, most of them probably just don't know a) that they can and b) where to do so. So enforcement isn't the issue at all, it's ignorance.
Making it clearer to first time users that the checkmark is there and usable would probably fix this whole issue. With all the other link commands on the page (add comment, was this useful, etc) many new users may assume that clicking "was this post useful to you" is how you approve an answer. I certainly did.
Easy fix for this might be to show a popup with an arrow to the checkmark after the first time a user sees a first answer to a question he or she has posted. Popup would say something like:
Is this the best answer? If so, click here.
It should appear on every answer's checkmark until the new user has chosen one, and maybe the text should also indicate it's okay to wait for a better answer if this isn't a good one.
The current checkmark blends in so well with the UI that your eye simply doesn't go to it, doesn't look like a central important button to pay attention to. Tweaking the checkmark design itself may also help.
Could this be done?