"In sum, something "fundamental" changes when you want to go fault-tolerant and tolerate node failure in an asynchronous system. When you combine faults and full-asynchrony, you get the FLP impossibility result. That means you lose progress! That is why Paxos does not guarantee making progress under a full asynchronous model with a crash failure."

This is unclear to me. Egalitarian Paxos guarantees progress under a full asynchronous model and doesn't have the dueling leaders problem. So this looks like a weakness of standard Paxos itself, not a fundamental problem.