What's the exact reason a pod-template-hash is added to the name of the replicaset when a deployment is created?

Correct, the documentation states this really well:

The pod-template-hash label is added by the Deployment controller to every ReplicaSet that a Deployment creates or adopts.

This label ensures that child ReplicaSets of a Deployment do not overlap. It is generated by hashing the PodTemplate of the ReplicaSet and using the resulting hash as the label value that is added to the ReplicaSet selector, Pod template labels, and in any existing Pods that the ReplicaSet might have.

This is necessary for a bunch of different reasons:

• When you apply a new version of a Deployment, depending on how the deployment is configured and on probes, the previous Pod / Pods could stay up until the new one / ones is not Running and Ready and only then is gracefully terminated. So it may happens that Pods of different ReplicaSet (previous and current) run at the same time.
• Deployment History is available to be consulted and you may also want to rollback to an older revision, should the current one stops behaving correctly (for example you changed the image that needs to be used and it jsut crash in error). Each revision has its own ReplicaSet ready to be scaled up or down as necessary as explained in the docs