The main objective of the big Mac index is not to measure inflation, it's to measure purchase parity power by using the price of something that is available in almost every country and has a very standard quality.
Just consider the same country at two different points in time as two different countries and the distinction disappears.
Unless the country in question only consumes big Macs, using that index as a measure of inflation would be a terrible idea.
According to the Arizona Ice Tea index, there has been NO inflation.
Costco Hot Dog feels the same.
I know you're both joking, but the Big Mac is a global product, unlike both of those.
So despite it still being a joke indicator, it does tell us something useful (which is a sort super rough cost of living indicator).