Why does Bakemonogatari exclusively use katakana?
I strongly suspect the use of katakana here is just to give an archaic flavor to the typography. Historically (pre-WW2 or thereabouts), katakana was actually used in many contexts where hiragana is used today - not just for loanwords (note, though, that even today, katakana has other uses). In the same vein, the show's typography exclusively uses pre-simplification kyuujitai kanji rather than their modern shinjitai counterparts. 

Formal pre-war documents were frequently written in the "Monogatari style", so to speak - look, for example, at the 1890 Imperial Rescript on Education, which uses exactly the same style: kyuujitai and katakana.

I don't think there is any deeper meaning to the use of katakana, in and of itself. Maybe there is something to be said about the archaic-flavor thing viewed as a whole, though. (Personally, I suspect the thing to be said is just "Shinbo thought it looked cool this way".)