If you consider pre-crime to be a thing that actually exists.
Also, considering that the Mr. Mikune scandal breaking and his subsequent suicide is what causes Oriko to contract, and Oriko contracting is invariably what causes Kirika to contract, it seems reasonable to conclude that the scandal occurring at all (or, at least, breaking during March 2011) is temporally anomalous. Since Oriko contracted within a couple days of Sabrina showing up, which was 2 weeks into the loop, Homura should have had the time and foresight to defuse the Orikobomb regularly and entirely as part of her per-loop checklist, were she so inclined, but she doesn't-- because a time-stop drive-by is a hell of a lot faster, easier, more efficient, and more assured. This is what I mean about her seeing them as threats and not as people, and exactly why Sabrina is gallivanting across the countryside fixing everyone's problems so that bad things don't happen-- Homura's way doesn't lead to Good Ends for anybody.
You're making a
lot of assumption there, including the timeline. It's entirely possible, for instance, that the time gap between Mr Mikuni's scandal breaking and Oriko contracting is sufficiently large that there's no way for it to act as the flag you're suggesting it is. Similarly, in at least one of the mangas, Kirika contracts
before Oriko.
Furthermore, this is not merely precrime. Homura personally experienced Oriko and Kirika going all massacre-happy on her school and murder Madoka
even when she thought she'd won. That kind of trauma leaves a huge mark on someone, and for all Homura knows, Oriko contracting was going to become a constant in her loops after the loop where it first happened. She only found out it was anomalous after the fact.
In addition, you are failing to recognize the critical point: if Oriko manages to contract, she's
already a massive threat, so checking whether or not she's contracted is moot, since if she has, it's already too late to deal with it easily. And again, it's not a predictable event--if Oriko never made a contract in all of the loops previously, what caused her to make one in that loop? It's entirely possible--if not probable--that Homura never knew anything about Oriko's father and the scandal that led to his suicide. It's not like Oriko ever talked about it.
Homura is willing to do
whatever it takes to ensure Madoka's long-term safety and well-being. If that means murdering a couple of innocent people because they
might become massive threats to Madoka's safety (or Homura's own safety), she's willing to do that. This is, after all, the same girl who is willing to risk a scenario in which Madoka contracts, becomes a Witch, and Homura herself is killed before she can loop back to undo it, causing the end of the world. In her eyes, while it would be just fine and dandy to succeed in her goal without resorting to committing horrible deeds, realistically, if she can't accomplish the
one thing she dedicates
everything for without resorting to horrible deeds, then she cannot afford to hold back even that much if she wants any chance of success.
The reason Homura always fails is because Walpurgisnacht is just so overwhelmingly powerful and a hard counter to Homura's abilities. It's blatantly unfair--and it's implied that evacuating Madoka to another city doesn't even work, because Walpurgisnacht's target
is Madoka, not necessarily Mitakihara. The only conceivable solution, in such a scenario, is to build a big alliance of magical girls to all fight an overwhelmingly powerful opponent (quite possibly far away from home, at that) for no reward beyond trying to do the right thing. And magical girls are notoriously territorial, difficult to organize or bring together beyond small groups, and difficult to move around without stepping on too many toes. Compound that with the fact that Homura has to keep Madoka from contracting, Kyubey wanting to get Madoka to contract, Mami wanting to get Madoka to contract, Sayaka's tendency to contract, Kyouko's bad blood with Mami, and Mami's own fragility and faith in Kyubey, and you get a situation in which you'd need to be a social expert just to handle the
local problems--and Homura was, even at the best of times, before all of her worst trauma, socially awkward and crippled by extremely low self-esteem. Sure, she could gain experience and skill over time, but when that time is filled with trauma and having all of her progress continually undone via looping, it takes a herculean effort (and the right mindset, which can be impossible to obtain without outside help) to not let the trauma hamstring you socially before you gain the necessary skill and experience.
