Why is the sound "cha" spelled as ちゃ rather than ちぁ?

Question

I was wondering why is the sound "cha" spelled with a ゃ rather than a ぁ.
きゃ, for example, is "kya"; so shouldn't ちゃ be more like... "chya"? The same goes for しゃ.
I suppose "sha" and "cha" kind of already sound like "shya" and "chya", respectively; is this why or is there another reason?
Additionally, is there even such a thing as a small ぁ, if ゃ has this role anyway?

Answer 1

This is far from being a silly question. For one thing, the half-sized vowels (ぁ、ぃ、ぅ、ぇ、ぉ） didn't actually exist in the first place. They are mainly used while writing down a spoken sentence where the speaker insisted on the vowels, even more than the actual word would require. For example, you could find the sentence 「とぉぉても嬉{うれ}しいです！」 in a manga, that would mean that the character strongly insisted on the お sound in 「とても」. In English you would simply report that as "I'm veeeeery happy!".

Now, going back to the main subject. The Japanese is initially an only-spoken language, their writing system is entirely taken from the Chinese, even the kanas, which are all largely simplified kanjis. In our case that matters because even before their writing system was invented, the sounds "cha", "chu" and "cho" existed, but not "che", "chya", "chyu" and "chyo", so the "cha"&co. took their place in the writing system. Why bother to create a new notation for something which works the same way as the other consonnants when there's a system which works just fine? Of course, the same goes with the sh- (and its j- derivative).

Hope my explanations were clear enough, I tried my best for explaining a Japanese fact in English, while being French.