This would be a very nice addition to the site. Particularly if we could set it on the Ask Questions page so users can attach a small sample file if their problem is too wordy/hard to explain.
There are many pros to this. The main ones being that we get centralized location for users of the site to upload their test files and we reduce the cases of link-rot.
This site is supposed to be a collection of self-contained answers. Having users come to a question weeks or months later and finding dead links would be rather bad/inconvenient at the very least. It would also be nice to not keep asking users to attach files to their posts or recommending file sharing services.
Obviously, there will be many wrinkles to iron out, such as accepting arbitrary files, attribution etc. We already have a strict policy in place for blend files and our moderators and avid users will no doubt watch these very closely.