It’s not latency, it’s throughput. Broadcast and incast network communication patterns in the LAN kill throughput, and are present in any quorum protocol. Atomic broadcast protocols like chain replication or LCR which use strictly sequential communication patterns (via chain or ring topologies) have much better throughput in LAN environments than Paxos/Raft (except for Ring Paxos, which requires IP multicast). In addition, because they outsource group membership and failure detection to a separate (likely Paxos-based) service, they require only f+1 members to tolerate f faults, rather than 2f+1 (see Lamport et al’s Vertical Paxos work). But they have two main downsides relative to Paxos/Raft-like protocols: latency grows linearly with cluster size and is bounded below by the slowest node (so they aren’t a good fit for high-latency WANs), and as noted above, they can’t “self-host” like Paxos/Raft.

PS Apparently my previous comment outraged the HN hive mind, judging by downvotes. I find this hilarious and revealing given that all I’ve said is obvious to any actual distsys researcher (ask eg the HyperDex or FawnKV folks about why they chose CR instead of Paxos). And at one large cloud provider I worked at, this was taken for granted back in 2012. Apparently “distsys” pop culture has yet to catch up.