Bitcoin's price advantage over traditional payment processing options is not because it is cheaper at handling data. On a bit-for-bit basis, it is radically more expensive. (~$6k per megabyte at the moment?)
Bitcoin's price advantage is that Bitcoin declares out-of-scope the services which contribute most of the price, which are a) collecting massive install bases on both sides of a truly staggering number of markets, b) providing trusted environments for commerce to happen and c) mitigating many forms of risk within those environments.
You can, today, get a piece of plastic issued to you by an AI algorithm which will judge your character in single-digit seconds. You can then take that piece of plastic, literally fly to the other side of the world, and buy lunch with it, in the near certainty (in the first world) that there will be many lunch options that will honor it. You can then leave the plastic in the foreign country attached to a note which says "PLEASE STEAL ME!" You'll arrive back home to discover your card stolen, canceled, and reissued, at no cost to you.
This adventure will cost you the price of lunch plus about 5~8%, which will shock you because normally (domestically) the magic plastic costs you negative amounts of money, since domestic use of the payments network and dispute processing gets paid for entirely by merchants (whom it costs ~3%).