You realize, right, that Mami's OPness hasn't a whole lot to do with her being a 'veteran,' right? Aside from Miss Mori I-hope-that's-not-a-Rule-Breaker-you-have-in-your-pocket1 Rin, the rest of the Sendai group has been skirmishing with Isshinomaki for about as long as long as Mami has been contracted, with the additional 'fun' of stomping on the University girls (and some others) for about half that time. And given Akiko's fixation on hoarding grief seeds, they were probably hunting witches themselves, too.
So why is Mami so good in a fight? Her wish. While we don't know the exact wording, it was apparently something about being connected to life. That helps explain the ribbons thing (if her happy place wasn't explanation enough, anyway), her ability to target stuff behind cover, and it may help her in both dodging and aiming attacks. Plus the whole looks-like-a-choreographed-number thing she and Sabrina sometimes do, especially if you aren't inclined to chalk it up to ship tease.2
So I guess I'm saying she may have a Spidey Sense, if more subtle, but no less broken. And just like Parker's, it fails at dramatically appropriate moments. And she doesn't get those horrible headaches when something life-threatening and unavoidable shows up.
1Yeah, with her name being a Fate/Stay Night reference, the fact that her transformed outfit is a robe & mantle, and her weapon a funky looking dagger? It all screams "Medea" at me.
2 Go ahead and hit me with ye olde heretic stamp. In addition to the whole Mami trauma thing there's the also creepy thing where Sabrina is, as far as we can tell, a week or so old.
