*Counts Hayate's Wins* Oh crap....
On one hand, I could say that leaders aren't supposed to be on the front lines and that Hayate is more of a DPS/Area of effect attacker than a direct combatant. On the other hand, that just isn't really that exciting. So what's left is to showcase her command abilities and wits, which is a bit hard at times. Not everyone can be smooth like Gendo Ikari.
We are told that she is one of the most powerful when it comes to raw magical power, so a win against a credible opponent here and there would help. Other unique abilities besides beam spam would help; considering she should have tons of abilities at her disposal. Maybe she's not subject to the limitations that other people have. But, I guess it's the nature of any show/movie/story to relegate "important fights" to main characters only.
For example, Vita quickly established how strong she was in the first episode of A's. And not in the cheap "haha, I have some random power that nullifies all your abilities!", but in the sense that shows that she is clearly superior to Nanoha at that point. Nanoha can put up a fight but ends up getting crushed.
Chrono as a competent leader is also pretty clear; since he was young he was always serious and efficient.
It's the kind of stuff that makes us disappointed about stuff like no Lindy vs Precia in movie 1st, etc. Show, don't tell! Especially when you say their powers are extremely awesome and out of this world.
On an unrelated note, that reminds me of many a anime where someone pulls out some super technique that you wonder why they just didn't use in the first place.
Don't hold back, folks! The franchise has long run on rule of cool to give excuses for characters to show off. It's only fair Hayate gets more; maybe in Movie 3rd Strikers or what not.