Are Sugar cookies (that are iced with Royal Icing) suppose to be crisp all the way through or have a softer center? Or is it just a matter of personal preference?

TIA!

You bake them according to your preference. Many like to bake them till they are just set with no browning, which will make them softer. I personally like the flavor when they are allowed to bake a bit longer till lightly browned on the edges, which makes them crispy.
The truth is that they do get softer in storage as well as when topped with icing.