@Reverencia
Danaos said it best, I think; the majority (if not all) of these stories are not worth keeping and usually involve at least one scene in which two kittens end up having sex. The only games of these kinds with high ratings are, I believe, troll games specifically made to screw with the warrior cat author (I refuse to believe that there is more than one person making all these stories) by satirically mocking his work, or games that have been upvoted hundreds of times by mysterious guests.
Now, this is not to say that a good Warrior Cat game cannot be made, it is simply not being done as of yet.
Anyway, here's my (Personal, and then objective) rationale:
Personally? I do not like fanfiction stories and the fanfiction genre in general, if you are too un-creative to make your own story and have to borrow the majority of it from something someone else has already written then I find you to be an unimaginative author; therefore I do not care for the blow that this would deal the any future Warrior Cats authors who want to write fanfiction about the show.
Additionally, I do not care for the show itself (it is a ridiculous concept that i'm fairly sure was just used to sell plushies) and so I do not care if these fans have their stories deleted, regardless of its "quality".
This author has been plaguing the site for too long and his work should be deleted, as should all work of his kind.
Also, frankly, I don't care about the feelings of some Warrior Cat fan who wants to make a storygame about it.
Now, objectively?
Well, objectively, the issue is not the Warrior Cats stories at all, they're just another small group of troll stories among the massive wave of troll stories that we receive every single day, they only receive our community's specific hatred because while the other mass of stories are an incohesive, unrelated mess, the Warrior Cats stories are prolific enough and have the same general theme (Warrior Cats, enthusiastic kitty porn), giving us something to latch onto.
The issue here is that the standards for what makes a certifiably unpublishable storygame here are far, far too low. Any story (regardless of whether or not it meets the standards set here) that has been published for at least a week (plenty of time for members to rate it) and has consistently kept a score of 1 should be automatically unpublished or deleted from the site (I specifically requested this feature in the wishing well before but it was refused, I don't think it will change now but it is the truth, the lowest possible rating being consistently kept is reserved for the very worst story games and this should be the biggest factor taken into account when deciding whether or not to delete it). Bad stories in general, not just Warrior Cats, need to be removed.
In addition, banning that specific type of story will not be a good idea, as there is a chance (however small) that one day, an author who genuinely cares about what he's going to write shows up on the site and tries to write a Warrior Cats story that will be a story dedicated to the series that he loved as a child, and that this story will be both enjoyable and well-written. To eliminate the chance that we might one day have that story is not a good idea, and should not be done.
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Now, I addressed the first two points you said we would need to be comfortable with - but not the third.
Doing this will stop the Warrior Cat stories we already have, what it will not do however is stop the author making the troll stories from making more troll stories (just, you know, not abut Warrior Cats). The trolling will continue, just in a different form.
That is my rationale, take it as you will.