Stale replicas are a "stop serving requests from a particular region" problem. We pretty aggressively monitor these and consider things broken if replication is lagged more than about 10s.
One thing about running thousands of DB clusters (which we did at Compose.com before this) is, these problems exist even without geo replication. And they exist at such a scale that you have to be good at handling them. Geo replicas are _more_ prone to these kinds of issues but we already had to be good at handling them.