I'm a soon to be math graduate student and thought that this site would be a good learning environment for my extracurricular endeavors. Through my experience here, I've come to realize that a lot of the more reputable users are very quick to answer questions with seemingly perfect information which discourages me from continuing learning through answering questions on this site. In my opinion, the more reputable users should let some of the less reputable users answer questions for their learning benefit. Is this an inappropriate thread? Am I being unreasonable? What are some of your thoughts and concerns? By all means, close the thread if I am off course.
(This was going to be a comment on Carl Mummert's answer, but it started getting too long.)
A long time ago I made the same decision as Carl to back off from giving quick answers to relatively easy questions. I haven't always kept to it, and there are certain tags (e.g., linear-programming) that often go ignored but that I do know something about and so will jump in with a quick answer anyway. But for the most part, I think there is a lot to be learned from trying to answer questions, and I think it serves many of the learners on this site better if those of us with more knowledge back off from time to time from giving the quick answers. It's easy to say to just ignore answers that appear rapidly, but it's much harder actually to do it.
There is also the reputation issue. I think most of us have a love/hate relationship with rep. One of its more positive functions is that it helps people feel like they are a part of the site, that they have more of a stake in it. For those of us with high rep to jump in quickly with answers a lot of the time retards the process of newcomers building up rep, which means that fewer people feel like they have as much of a stake in the site. That in turn prevents the math.SE community from having as broad a base of regular users, which I don't think is as healthy for the site in the long run.
(While I'm editorializing, I try to be profligate with my voting partly for the same reason of helping others feel more like they are part of the site.)
So, while I would never want to see anything like this policy imposed, I would at least encourage other high-rep users to think about pausing before giving quick answers from time to time.
The fact that people posted answers should not deter you from writing your own answers. Even if you don't post them at the end. The process of writing an answer can teach you a lot about how much you understand something, and even more so if you write something which is intended as an answer.
If you wrote an answer to a question and you feel that you did a good job, post the answer. It's unlikely that people will get mad at additional answers.
I know where you're coming from and even though one also learns by answering questions, I believe the main way to learn from this site is by having our own questions answered. There are both advantages and disavantadges to what you suggested, however considering what I stated above, I believe it's better to keep things the way they are. Just my 2 cents.
No one wants answer-quality to suffer. Maybe the way for the @Carl Mummert magnanimous policy to catch on is in the incentive power of the scoring.
Suppose for example that answering a 10-day-old question with 1000 views scored significantly more than a 1-day-old question with 10 views. Then sage users would be gently and organically coaxed away from the low-hanging fruit. And noobs could cut their teeth on the easy stuff. I'd rather sages were thinking more about the hard stuff anyway.
Maybe this might help relieve compulsive answering syndrome too.
I just want to echo some of what other people have said. When I started here, I definitely wasn't very fast. Even with simple questions that I should know how to solve, it took me a long time to compose an answer. And by the time my answer arrived, other people had already answered the question.
I would encourage you to just answer anyway. This site isn't about being the fastest, it is about giving good answers to questions. If you can learn something from giving an answer, then I say: just do it. With time your answers will get better and better (and you will be faster). One thing that happened a few times to me in the beginning was that even though I was slow and I didn't feel like I had the best solution, my answer was still picked as the "best". Now I wonder if maybe my inexperience actually made a better answer.
You have probably also seen lots of quick answers that actually aren't that great answers. I have definitely been guilty several times of quickly posting an answer that turned out to be plain wrong. Or maybe I had not actually read the question in detail and I was not even answering what the OP was asking.
So just keep going!
I would say if you type up an answer, and you feel good about it, may as well post it. It is not like you are trolling. You are a mathematician. If for whatever reason you don't like your answer or see someone else post something beautiful and quick, maybe you can learn something from their answer and its simplicity or whatever it is.
I think you have something to gain and not much to lose by posting an answer.
I agree with you, @Rustyn. What Yuan says is true, but I think that huge lot of learning can be done by struggling to answer questions.
I think it'd be a good idea to have at least two separate answers sections in each thread: one for greenhorns (say, up to some 1000 points or so), and another one for more experienced ones.
Yet I've no big hopes this will ever occur: one would expect this site would require from people signing up to give at least their mathematical level (high school, undergraduate, graduate...), in order to know what level, more or less, of answer can suit him better.