It’s much easier to understand Paxos as a read-modify-write transaction. I wrote to Lamport about it. Here’s part of Lamport’s reply

It’s nice that you found an apparently new way to explain Paxos, but don’t expect everyone to find it helpful. “Grasping” or “intuitively understanding” an algorithm really means giving the reader a warm fuzzy feeling, and different people get warm fuzzy feelings from different things. What really matters is not warm fuzzy feelings, but the ability to rigorously prove that a correct algorithm is correct, and to find the error in an incorrect one.