I think I see what you're going for here. Kind of a text based version of a MUD (Multi-User Dungeon) or MOO (MUD, Object Oriented), where people with a common interest (like a particular fan fiction universe) could log in and come together to act out stories. Hence the natural connection people make to role-play. I participated in this sort of thing (back in the 90s, woohoo), where one could take on the character of Giles (from Buffy) or Sailor Mercury (from Sailor Moon) -- or simply be a generic person living in town, as my Alison Vunderlande character was. Yeah, I played as all 3 of those.
There's also a strong link here to the "Play-By-Email" format (which I did in the 2000s), where a bunch of people (with powers, or in a universe of some sort) email back and forth as coordinated by a GameMaster, who would guide the plot - and call for die rolls as needed. (We all had character sheets, so to some degree our successes and failures were random.)
Based on that, I see two main problems with the website:
1. The Structural/Out-Of-Character problem people have pointed out. If you're taking on a role, what you say as a character may be different from how you feel as an author. For instance, good stories usually need a villain, but would anyone ever want to play the villain forever? It's also all too easy to take something personally, particularly if someone starts perceiving you as a villain character and you're sitting there going "I... didn't mean it that way at all... wow, sorry..." Related to this is having no oversight. Am I allowed to write that I beat you up? What if the person on the other end of the keyboard is a woman in an abusive relationship? Am I allowed to power pose you into a tree? What if you hate heights? We just don't know, which (at least for me) is dodgy enough to me away, because I'm the sort to worry if I'm doing the wrong thing - and "wrong" is different for everyone. The original MUDs had the "OOC" rooms - or at the least a +finger command where you could write something like "if you power pose me, we're never playing together again". Also, if someone has a Real Life emergency, and has to stop playing for a few weeks - they have to make up a reason for their character to be away too?
2. Attrition. An easy counter argument to "1" is that a person merely has to read the back logs, and then they WILL know how to act with the various other people, and that they'll have a sense of people's triggers and who to interact with. But the longer a site like this goes on, the more back logs that creates, and the longer it will take until a person can immerse themselves in the game. (I also notice that to read the stories, I have to scroll down to the bottom and read up. This makes sense for something ongoing, but is awkward.) Aha, you say, but a new student is fine, and they don't have to know everything. Highlighting particular stories, as you did, is a good idea. But when you get a new person every couple weeks, doesn't that wear down a bit on the regulars? The ones who have already been through that, and here we go again? Cliques forming is kind of inevitable. And that can also make it difficult for newbies.
Don't get me wrong, it's not necessarily a bad idea, but I'm not sold on the format. Then again, I'm referencing 90s stuff, so guess I'm kind of old-school.