I’m thinking it’s probably this. Walpurgis was always the game breaker in the various timelines. We also didn’t see what happened to Mami after the Oriko battle. In general, as per “Word of God” (Gen Urobuchi), the following events are almost unbreakable if they occur:
Mami will have an emotional breakdown, resulting in her killing other magic girls or killing herself, if she discovers the truth about the Witch System. Mami is already emotionally unbalanced at the start of the story (she’s just really good at hiding it), and this last bit always pushes her over the edge. If Mami encounters Madoka and/or Miki before Homura does, Madoka and Miki will want to become magic girls at some point in that timeline.
Miki will become a witch after about a week, if she becomes a magic girl. Miki is a poor magic girl: she cannot handle the burden of “energy management” to prevent her soul gem from becoming polluted. The fact she’s unable to “bottle up” her emotions is a negative as well, since being highly emotional quickens the process of soul gem pollution (hence the reason gals like Mami, Homura, and Kyoko can avoid it for so long). Miki’s situation is to show that Kyubey intentionally picks girls he knows will become witches in a short period of time.
Madoka will become a magic girl if she witnesses the final battle against Walpurgis. Mostly because she can’t stay on the sidelines as she watches others die in vain and Kyubey is such a manipulative bastard. Because Madoka is so emotional, she is unable to handle the process of soul gem pollution, and thus always becomes a witch. In the first dozen or so timelines, Madoka dies or gets defeated in the final battle against Walpurgis. After about a dozen more timeline reboots, Homura inadvertently makes Madoka powerful enough to defeat Walpurgis, but she still becomes a witch sooner or later thereafter.
The core problem Homura has, is that she can’t defeat Walpurgis alone. She has a powerful magic ability with time control, but lacks offensive power since she doesn’t get a magic girl weapon. On the face value, Mami would be an excellent choice – she’s considered one of the most powerful magic girls in the setting – but cannot handle the truth and becomes a lose cannon. Miki is way too weak. That only leaves Kyoko, who is too difficult to recruit without somehow proving magic girls become witches… which usually requires Miki being a sacrificial lamb.
The Puella Magi PSP game offers a perfect end timeline, in which Walpurgis is defeated without Madoka becoming a Haxxor Magic Girl and the witch system remains in place after the battle… but it requires Mami being kept in the dark about the witch system and Homura caring about all the girls at once instead of just Madoka. Naturally, this was provided as a “fan service” for people who love the series… it’s not canon, since there’s too much happiness. 
EDIT
On a totally random point, if Narg was in the Puella Magi universe and Kyubey granted me a wish, I’d want twincest. 
Since Kyubey rigs the system, I’m sure I’d witness said twincest die in a witch attack and become so despaired I’d be a witch too: the Witch of Eroge. My barrier would be like an abandoned rotting warehouse with mountains and mountains of ero games everywhere, but none of them are twincest titles (since each witch has something she wants but can’t get). When magic girls come fight me, it be a tentacle familiars would face them. Hmmm… I’m sure there’s a doujin out there with this plot line… I just need to find it.
