I was already assuming a perfectly idealized p2p network that had no overhead or sub-linear scaling. I've done as much to explore the space of efficiency gains in this kind of system as any two other people combined here, come on. Please don't try to play off that I don't know how the system works. Decentralization has inherent costs.  You're not saying anything to escape that. It's not good enough to just say "broken broken" when reality doesn't behave like you wish it did.  I also wish there wasn't a tradeoff here, but it doesn't make it so.  (And to be clear, I think there is some amount where the costs are insignificant and not a concern and that cutoff changes over time; it's only the unlimited view which I think is clearly at odds with strong decentralization and risks disenfranchising the actual holders and users of bitcoin; people who weren't signing up for a system controlled by and operated at the complete whim of a few large banks ('miners'/pools)).