> For values that don't have a natural merge function (or where you don't want to bother writing one), would it make sense to sync update logs instead?

Yes, in fact you can implement this within the current framework, for example with our group chat River, each room state maintains a list of the N most recent messages sorted by (approximate) timestamp.

The idea is that you can adapt the merge logic to the needs of the specific application, and I think a time ordered event log will be a common pattern.