The essence of the proof is simply that chains cannot distinguish transfers that are part of Liquifinity trades from other on-chain transfers by those same users themselves. For one thing, this means no smart contracts whatsoever. For another, it provides “censorship resistance” — a significant aspect of the blockchain ethos.

(Without property 2: extremely limited trading pairs because chains must have identical cryptography in common; custody risk from smart contracts; cost of smart contracts; censorship by chains.)