Why is the mandarin word for 10 pronounced Shi(r)?

Because the Chinese people didn't adopt the pinyin system until much much later--in fact my grandparents didn't know pinyin (if they were still alive they'd be in their 80's right now) and so they tried to give Chinese words a matching phonetic spelling after everyone had been speaking the language for thousands of years. And they wanted to keep the stuff consistent, it would be weird to suddenly see a "shir" after a bunch of words with clean vowel endings.