Comments - Setting Up Replication
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You actually can use a "blank" slave and set it up to replicate every event that has happened on the master since the was blank too. Although technically possible, this would require that you 1) can identify the exact transaction on the master that was equivalent to the clean slave's current state, 2) have saved all the binary logs on the master from that blank state up to the present, and 3) have the time to replay the master's transaction history on the slave.
So your intuition is correct. It's just that practically speaking, letting the slave replay the master's transaction history from installation forward is a lot more difficult and time-consuming than starting from a recent backup.