Pinyin’s usage of the letter C for /tsʰ/ (not /ts/ as the person you’re replying to says! The difference is subtle but it’s there.) was apparently modeled on a previous romanization system called Latinxua Sin Wenz, which was created in the USSR. I’m kind of talking out my ass right now but from what I half remember these were the motivations for the choice of C for /tsʰ/ in Pinyin:

1. Conciseness. Pinyin was ultimately created for Chinese people and not for Yankees studying Chinese, so whether a particular design decision made sense to a particular group of foreigners was less pressing than shaving off a few letters here and there.
2. Pairs and patterns. Letters representing voiced sounds in English always represent unaspirated sounds in Pinyin, letters representing voiceless sounds in English always represent aspirated sounds in Pinyin. Digraphs ending in H always represent retroflex sounds, i.e. ⟨zh⟩, ⟨ch⟩, and ⟨sh⟩ for /ʈʂ/, /ʈʂʰ/, and /ʂ/, and you may notice how if you get rid of the H’s you get the corresponding alveolar sounds Z /ts/, C /tsʰ/, and S /s/.
3. Precedent in other languages. The letter C makes a /ts/-like sound in a LOT of languages, in particular in Albanian; in Slavic languages, including in many romanizations of Russian, where /ts/ is spelled in Cyrillic with the letter Ц; in Esperanto, which was having a bit of a moment in China when Pinyin was being devised; and to some extent in German and a number of Romance languages old and modern; as well as in Early Middle English, which is where we get the Modern English “soft C” from. The magic word here is “palatalization”, especially palatalization of historical /k/.