I agree with the CAP theorem and it applies to my example. In my example replication only provides a backup copy of the data and is not used by the application,

I agree with the CAP theorem and it applies to my example. In my example replication only provides a backup copy of the data and is not used by the application, that's why it's active-passive (provides reliability). This configuration provides the highest level of data protection that is possible without affecting the performance of the master database/shard. This is accomplished by allowing a transaction to commit writes to the master database. The same transaction is also written to the slave, but that transaction is optional and written asynchronously. Two-phase commit is not performed.