In contrast distributed applications typically at best will have a write through cache where global consistency happens all the day down at the actual data store. Exploring the idea of distributed MOESI where one client, because they had the permissions to write something in the first place, can then be the owner for that database row as it's still being flushed out seems like a great basis for a distributed system that might not even need the dedicated datastore at all anymore, but a sea of clients participating in coherency and replication.

Modern commercial distributed file systems do the type of caching you’re talking about. More generally, a Distributed Lock Manager [1] gets you halfway there. You’re right that a write-through cache is still necessary to achieve redundancy requirements, but especially in the context of file systems you can often coalesce local edits until the user explicitly issues stage equivalent of a flush operation, and only do the write-through then.

[1] https://en.m.wikipedia.org/wiki/Distributed_lock_manager