I don't want to have the parent VM on local storage, but that's something I ran into at a customer and I wondered if that was supported. I was under the impression that the parent VM needed to be on shared storage so it could be copied to a replica on each local storage. But that doesn't matter if it is copied over network, it could be anywhere. The VDI-hosts would only need to have local storage and no shared storage whatsoever.
When deploying a new pool or when updating a pool, copying over network is very slow. It would be faster using the shared storage.