Annoying, isn't it?
You shouldn't run into this problem if you use the Pointer tool (the black arrow) to move Smart Shapes on the canvas. But you will run into it if you use the Subselection tool (the white arrow). Where I tend to run into this alert message is when I option-click to copy an object, as the Option key also acts as a shortcut to the Subselection tool, and I wind up accidentally subselecting a portion of the Smart Shape.
The fact that you may not be able to edit a property like corner roundness afterwards is exactly what this dialog is trying to warn you about. If that's the case, you may want to click the Cancel option at the first appearance of such a dialog, and rethink what tool you're currently using.
Having said that, in a flow like this, I am still getting this message:
In order to stop the message, after choosing the Pointer tool, I have click on the canvas and then start moving the object again. Might make sense, but still annoying.
Yeah, that's a good point. After accidentally subselecting a Smart Shape (and choosing Cancel), it isn't enough to just switch to the Pointer tool. Clicking once or twice on the object with the Pointer tool should work to select the item properly. Otherwise, you can also click on the canvas to deselect the object first.
Take a look at the object on the canvas; its appearance will give you a clue about what's been selected (or not).