Of the many things that can go wrong, the one I would be most worried about would be replication lag causing the disk on the primary to fill with WAL logs bringing down the primary, or if you have limited the WAL logs, the replica not being able to keep up and detaching from the primary causing stale reads.

Also long distances will make replication latency increase so unless _all_ requests are sent to the primary region you will likely have a read after write state data situation unless you go out of your way to ensure consistency