It's not just a name the author randomly chose for the sake of having something to call the story's central group. Kishiar canonically put a lot of thought and care into naming the Arcane Legion, as he's done with everything he's named so far.

And he even explains how and why he named it that in the novels (Chapter 798):

"I named it to imply a power that was sometimes magical, sometimes a weapon."

"I initially wanted it to mean that the Awakened are no less than mages or Sword Masters and possess a power as great as the combination of both."

How would 'Cavalry' relate to either of Kishiar's intended meanings?