I looked up 釈迦 at goo辞書 and noticed that there were two alternate readings presented for this word: さか and しゃか. The さか reading is given as being 『「しゃか」の直音表記。』, so these two are clearly the same lexical item, just with different kana representations.
I then looked up 直音 and found that this term basically refers to any mora that can be written using a single kana - so it includes あ・き・す・て・の but excludes きゃ・しゅ・ちょ, as well as non-standard two-kana morae like グァ. One can respell 拗音 (i.e. non-直音) as 直音 by "removing" the middle phone, e.g. /sha/ → /sa/, /myu/ → /mu/, etc.
So I understand what 直音 are, but I do not know why one would choose to take a perfectly good word like しゃか and then rewrite it using only 直音 so that you get さか. When, historically, did people prefer 直音表記 and why? Are there some types of words where the use of 直音表記 is particularly common, e.g. Buddhist terminology?