I frequently come across a question that was asked years ago, for which someone wrote a really good answer, but the answer was never "accepted". In some cases, the answer would make an excellent reference answer like this one, but we can't create a canonical reference question out of it because the answer was never accepted.
In cases like these, should moderators accept the answer? If not, how can we turn these into reference answers?
Only the OP can accept answers. There's nothing any of us can do about the check mark. That doesn't necessarily mean it can't be a canonical question; we can still edit and upvote one great answer. The check mark isn't required for that.
You seem to be confusing the purpose and meaning of the acceptance mark.
The meaning of the acceptance mark is "this answer was truly useful for me, the person in the problematic situation". This is different from the meaning of votes, which say "I consider myself an expert in the field and I am convinced that this answer is useful".
The reason we need both is that none of them actually means "this answer is correct". Sometimes the experts are wrong, because they fell for a convincingly-sounding-but-wrong answer, or simply because prediction is truly difficult and solutions which sound promising turn out to not work when tested. Sometimes the OP is wrong, because sometimes OPs don't (or can't) test answers and tend to hold on to wrong assumptions, so they disregard the correct answer. In any case, both are just evidence, not proof, that the answer is correct. And having two independent channels for such evidence - one being the OP's opinion as expressed in the question mark, the other being the community's opinion as expressed in the votes, is useful.
If we were to give moderators the power to give accepted marks, there are two possible scenarios. They would either place it on the answer the community likes, or on some other answer that does not reflect the community's preference. If they place it on the answer preferred by the community, the information value of the acceptance mark is lost, because now it carres the same information as the vote maximum. If the moderator places it on a different answer, the question comes up, why should the moderator have this special power of placing the question mark? Generally, knowledgeability on the topic is not a requirement for being a moderator. Also, even if the moderator is knowledgeable, individuals make mistakes. The OP has the power to accept because they have the special qualities of 1) knowing the problem better than everybody else, and 2) being motivated to empirically test different solutions until they find a working one. None of this applies to a moderator.
Having argued why it makes no sense for the moderator to place acceptance marks, I would like to also mention that there is nothing wrong with questions not having accepted answers. The usefulness of the check mark is limited to the OP telling us "this is my favorite solution". The presence of this information is convenient, but its absence is not tragic.
As Cascabel mentioned, canonical questions also don't require the presence of a checkmark. For them, it is even less useful. They are meant to reflect the opinion of the community, so there, the information about community opinion (the votes) is what counts.
