"The only reason I care is if I didn't purchase the right zone the turnstyle won't let me exit at Kings Cross."
No. There is no zonal coding for a paper ticket. The cash fare is a flat fare to any tube station in London - it doesn't matter if you change your mind while on the train and get off somewhere else - tge ticket is valid. You pay the same cash fare whether you go one stop to Hatton Cross or if you head to central London (oyster / contactless pricing rules are different and it'salways cheaper than a cash fare)