I would like to even close some of my support request's like help for email or setup and even some feature request because they either existed in some other way or has been implemented now.
Also many of the thread's have context of time in which they were created, things which were applicable in say August when I came on this forum and now are quite different. Personally I won't like to discuss on some of those threads now and would like to close them. If required, I or anyone else can create new thread and re-start a discussion.
There is another way to look at it
As per current privileges of users at level 4, user can almost do everything on the forum like pinning / unpinning, closing, splitting, merging topics (of everyone), creating /editing categories but then at level 3 he can't even manage his own created threads. As I grow up on the forum i want to start taking care of my own actions and then others.
So, it will be good if at level 3 he at-least get a control of his own threads to a larger extent.
Finally it depended on every forum and their category definitions and meaning they assign to closing / archiving topics.
Although I agree, it is can be a handy feature, but not really must or high priority one.