What use is "q" as a letter at all in English? It makes a "k" sound and always occurs with a "u" after it. Why not use it for the "tch" sound? (Which, btb, is different than the "ch" sound.)
"C" is about the same -- by itself it always sounds exactly like "k" or "s". Why not use it for the "ts" sound?
As for "zhou" -- in English, z is very similar to an s, but voiced. So in pinyin, zh is just like ch, but voiced.
Lots of languages do this BTW. When people from Wycliffe want to translate a Bible into an obscure language without a writing system, they first have to invent a writing system. They could invent all new characters, but why? All it would do is make that language hard to type. So they take the sounds that language has, and map them onto Latin characters. Sometimes there's an obvious mapping, sometimes not.
Look up Welsh's spelling for another example of this.