The questions below are intended to be serious rather than frivolous. I lack experience in distributed systems, but I do understand how Basic Paxos works and why leader selection is useful. Unfortunately, my understanding is not deep enough to fathom the questions below.
In the paper Consensus on Transaction Commit, page 8 (page 11 of the linked PDF), we have the following statement.
Selecting a unique leader is equivalent to solving the consensus problem.
If this statement is true, and the very purpose of Paxos to achieve consensus, why is Paxos itself not generally used for leader election?
Moreover, the same paper endorses the leader election algorithm described the Stable Leader Election paper.
If the two problems are equivalent, and the same paper endorses a different leader election algorithm, why isn't the other algorithm used for solving the general consensus problem instead of Paxos?