Byakuren uses magic, so wouldn't stuff like spells make sense for her?
Besides, things like spellcards weren't exactly unknown.
Also, the game itself could be a giant abstraction anyways
I mean, Reimu and Marisa should be complex barrages like they do in IN stage 4,
but since 2 sets of danmaku is too confusing for the player, the game abstracts it to shooting straight fast bullets
In the same way, since the game adopts spellcards, might as well have Byakuren use them for consistency.