@KPS live/warm migration between clusters is what we were discussing here. Yes, we do it routinely and it is a fantastic feature.
We have some VMs with more than 1 and 2 TBs of storage, so that takes ages. In that case, it is easier to assume some downtime and follow the continuous replication strategy, with the last copy done while the VM is powered off. The only advantage of this strategy over the live migration is that you retain a copy of the VM in the old cluster.
The ability to do a live migration but retain a copy of the VM in the old cluster, just in case, would be greatly appreciated. Best of both worlds.