It is not possible to move a featureclass in or out of a feature dataset in ArcGIS Pro without making a copy. This is different from the behaviour in Desktop 10.6 and all prior versions where you can move a featureclass in or out of a feature dataset without making a copy. I have contacted support and am told that this is by design.
My question is why is it not possible to 'move' a featureclass in Pro without making a copy and is this the way of things in the future versions of Desktop?
This whole thing came up for me as I found we were unable to move a registered spatial view into a featuredataset in 10.5/10.6/Pro as views in feature datasets are no longer supported. Much of our published geodatabase is built using views as it allows us to do things like rebuild spatial indexes during the data without having an outage. It would seem like feature datasets are on the out as they no longer are supported with views, have issues with replication and now you can't move items in/out of them.