Keep in mind that the goal isn't just to help the original poster, but also the goal is to provide a knowledgeable resource for future visitors for years to come.
All an accepted answer means is this: It's the answer that solved the original poster's problem.
This doesn't mean that you or I couldn't come along and write a better answer. The system is designed in such a manner that, if you have a better answer, you can add it. There have been times when I've seen an accepted answer that was targeted specifically at the op and left a lot of questions for people who, for instance, may not have a lot of experience with the subject and who would have benefit from a more generalized answer. Sometimes I've benefit the most from answers 2 to 3 levels below the accepted answer.
When I come across these posts, if I have more to add and happen to have knowledge on the subject, I'll post an answer. You can still help out future visitors by posting better answers, and you can still receive upvotes from posting an answer on a question where the op accepted an answer. The accept is a mere 15 reputation, but 10 upvotes on a really great beneficial answer can increase your reputation far more than accepts will.
Lastly, remember that accepts can be changed weeks, months, or even years later. Again, this is by design to encourage constant improvement. If you write a better answer, it's possible that the op could select yours. This is not a permanent operation.
In summary, don't be afraid to post an answer to a question just because you think the op is satisfied with the result. The system, as it's designed, is setup in a manner to encourage people to add better answers, and anything that highlights the fact that a post already has an accepted answer would just simply discourage others from answering, and would not support the goals of constant improvement.