One downside is that, if all your nodes are using the same application code, simply replaying the log might not help as all nodes might hit exactly the same bug with the same sequence of transitions.
[0] There's an overwiev of their infrastructure here https://youtube.com/watch?v=b1e4t2k2KJY
LMAX use synchronous replication in their exchange: https://www.infoq.com/presentations/LMAX
This is used by the Phoenix project's Presence module to provide a distributed notion of what users are 'present', but it's also used by others to do service location using hash rings, or implement a dht, etc. I've used it for master election and failover on a few projects for little services.