@Downunder skis of course wear out. The carbon fiber is glued together with epoxy resin and that resin holds the bits together depending on materials, heat, UV exposure etc. they all have a certain properly of how many cycles they last under a certain load but assuming the load applied and the conditions they are subjected to stay within a certain zone of typical use then I think you can make an assumption that most all skis will very gradually wear out and become softer with cycles but what will really wear a ski out would be outside of bounds amount of heat, physical damage, or excessive spikes in forces.
In regards to cores since all the cores start out as flat sheets of material I would encourage you to think of the core as a component of a sandwich like if it were an I-Beam the top and bottom sheets are connected by the core and that separates the material and makes the ski a composite structure where they act as one being bonded into a ski.
Don't think of the core as a ski shaped piece of material like if you could take the cores out and were able to ski on them they'd both just be floppy flat foam planks. Its the property of the materials when glued up to the outer skin and laminate that makes it a shape and gives it the properties but how that core reacts is as part of the sandwich. Consider the few "hollow" skis which have no core they still have a shape and properties.