If it sounds like sh, why is it written ch?

Because English ch has three separate jobs and this word was handed the wrong one. In native words it says the sound in church. In words that came from Greek it says k, as in chorus and character. In words that came through French it says sh, as in machine, chef and parachute. Pistachio belongs to none of those groups by descent. Follow it backwards and it runs Italian pistacchio, Latin pistacium, Greek pistakion, and behind that a Middle Persian word for the nut, and at every one of those stages the letters in the middle stood for a k. English is where the sound changed, and it changed without anything on the page changing with it. So pistashio is not a bad transcription. It is the word as it would look if the sound had been allowed to rewrite the spelling, and it is about four hundred years too late to be adopted.