Hmm... Kikaifan raises some good points. To them, I have come up with a possibly wild theory.
The classification which I posted came from Tiana, when she was talking to Subaru during the bath scene in chapter 5, page 7.
However, the Belkan system is know to be divided into 2 types: Ancient (which Hayate, Karim, Acoss and, I assume logically, the Knights use) and Modern (which seems to be a common type used in the TSAB, since their cadet training school allows cadets to select training weapons based on which system they're familiar with: Midchildan or Modern Belkan).
To begin with, I assume that Ancient Belkan users are very rare, as only Karim, Acoss and Hayate are considered to be users of rare abilities/technology; and assuming that Ancient Belkan is a forbidden or little-known school of magic.
If these assumptions are correct, then we can say that Tiana was referring to the Modern Belkan type, since it's highly possible she doesn't know about Ancient Belkan much. If so, we can also assume that Modern Belkan grew out from
one particular branch of Ancient Belkan magic, aka the physical enhancement branch that the Knights employs.
By this line of thinking, we can thus believe that Ancient Belkan is a far more extensive school of magic, and which might explain why Reinforce have shooting and bombardment spells like Mysteltein and Ragnarok. As to why the Knights don't show any use of other forms of magic, it might be because that they either were not required to know (aka not programed to know) or they didn't feel the need (I support the former reason).
My 2 cents
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