As for the idea... this would be like opening Pandora's box when allowing a thread for users to post their fan stuff in. Making such a thread for fans would inevitably mean that you have to allow non-fans to post in it as well... and that would open the door for hate videos, rotten content, flamable texts, etc... etc... etc...
Uh, *section and they can already do this, to be honest. No one is stopping anyone from not liking stuff. Something is stopping them from posting hateful content and flames, which are, well, the rules.
Making a thread in the AMW asking people to share their chosen fanart and fanfiction would not be that bad of a plan, and it really would not spawn hate, because it would be against the thread's purpose (besides still being against the rules), making your own thread to share your own fan-content would likewise be do-able, though making an entire section for this would arguably be unnecessary and might very well not get much content considering how little content is already being shared in the AMW.
Maybe the reason for AMW not being active is because people don't really think that their fan-fics aren't "Original" enough, being based off something.
If it's written or drawn by you, it's as original as it needs to be. People might not understand this, but then again, we have a user base that cannot differentiate between the popular media section and the AMW in the first place, so I can't really say it's the wording stopping them.
More so, I think fanart and fanfiction might get more attention, due to the fairly relate-able content, while many people might not be interested in investing time to get to know the original characters of the other patrons.