Suppose a question was asked 4 months ago and the OP was satisfied by a given available answer: Is there any benefit to add y own answer to the OP's question 4 months later?
Yes, if you have another way to answer the question posed, that you think has some merits, you should post it. The answers are not just for the OP. If the OP was satisfied, good for them; but think of the people who will be looking for that question later (depending on the question, there may be hundreds or thousands of them... or hundreds of thousands).
Users generally overestimate the importance of "accepted" checkmark. Just a few hours ago, I came across an answer that was accepted and upvoted, but offered a poor solution for the problem posed. Under it, there was a later answer with started off with a half-apology "I know this is resolved, but... " and proceeded to present the correct, canonical solution to the problem.
I did just that there and there. In both cases, hundreds of people agreed that it was a good thing, and in both cases the OP moved the "accepted" mark to my new answers, thereby marking his acknowledgement that the new answers made sense.
The SE people even designed the Necromancer badge to promote late answers.
In general, writing good answers always makes sense. Regardless of what the OP thinks of it.