I would go even further than NotTheDr01ds and say that the person asking the question is only tangentially relevant. If the question can stand on its own and doesn't need clarification, then the job of the OP (original poster, the person who asked) is done and they are not needed any more. They don't need to accept, they don't need to ever come back.
I don't know how many times I have been helped by random solutions I have found online years after they were originally posted as answers to someone else's problem. We don't answer for the person who asked, we answer for the thousands of users who will be seeing the question and its answers in the future.
As for accepting, again that isn't really relevant. Sure, it's a nice little rep boost and a nice little ego boost, we all enjoy having our answers accepted, but that's all it is: a minor perk. The accepted answer isn't always the best one (indeed, it is very often not the best one), and a question doesn't need an accepted answer in order to be counted as "answered". It just needs an upvoted answer. So accept marks are really unimportant.
All this to say that of course we should still answer old questions, you never know who will find them useful and the fact that our answer might never be accepted shouldn't even be taken into consideration. It just isn't relevant. We answer questions to collect a useful library of answers that can help all visitors to the site, both present and future.