Categories should be clear cut, but as of now there are a lot of different beliefs as to what constitutes a story's inclusion under a story arc category.
For instance, the Category:Bad Wolf arc is the second largest story arc category with 29 stories. Rose is included in this arc, but The End of the World specifically states:
The story also introduced recurring characters Lady Cassandra and the Face of Boe, and featured the first mention of the ubiquitous phrase "Bad Wolf".
So why is it included? Is it merely due to Rose's presence even though the actual "Bad Wolf" clues don't start appearing until The End of the World?
Then we find out what the arc means in The Parting of the Ways, which aired June 18, 2005. According to some users, this means because we found out the mystery behind the arc, the arc is officially concluded and no more stories published after that date can be added to the category. However, we have many stories under this category including Tooth and Claw because of the "something of the wolf about you" line to Rose and Turn Left due to the fact that it picks the arc up again by having Rose invoke "Bad Wolf" as a significant message to the Doctor about reality collapsing.
Complicating matters further, Shambala has noted in the past that some editors also think that repurposed footage makes stories retroactively part of an arc, as in the case of various shots repurposed to include Clara's echoes in The Name of the Doctor and then old TV stories were added to the Category:Clara Oswin Oswald arc. Looking at the category presently, those stories appear to have been removed again, but I feel the fact that this occurred in the first place (I think Shambala's comment was that it was a very abused category, although I can't remember which talk page she mentioned this on) still illustrates the need for clarification regarding story arc categories.
Category:Story arcs isn't helpful in that regard, but story arc says:
"Story arc" is the term that refers to a common thread in a series of stories, forming an overall "arc" throughout them. This can be a central subject that holds the stories together, such as Season 16 of Doctor Who.
I would conclude that revealing the mystery of the arc doesn't exclude stories published afterwards. If the arc is invoked/expanded at a later date, then that story becomes part of the arc due to the central subject. The Bad Wolf arc in Turn Left or the Clara Oswin Oswald arc in Blood and Ice are examples of this: they may have occurred later, but they're nevertheless connected by the subjects of Bad Wolf and Clara's echoes, respectively.
Similarly, if a story is intended within the time period of an arc and directly references it, such as Weapons of Past Destruction being a Nine, Rose, and Jack story and including a Bad Wolf Bargains sign arc reference at the bazaar, it should also be included in the category.
While I can't speak for Rose, it would seem that the Bad Wolf arc was counted on due to Season 4 incorporating it into it's finale.
Besides, I don't think the Story arc categories should be deleted due to their names being open to interpretation. Would it not be less time consuming to merely explain how a story is linked to the arc in the sub-category descriptions?
Up to you, if you want to do all that work, but it's not necessary. I'd like for CzechOut or Tangerineduel to formally declare this discussion closed, and once it is, then I'll do the deletion work for all, whether they all have delete tags or not.
No it wouldn't. That would include stories that have Bad Wolf featured as an Easter egg on a wall or as a part of the plot. We can definitively list those, which story arc cats are based on speculation and incorrect presumptions. Totally different.