While this is doubtless a real consideration, in all disciplines but ice dance you actually don't necessarily need to cut... something else I think a lot of skaters ignore, sometimes to their detriment, is that actually, one could just skate to a piece of music of approximately the appropriate length (and again, there really are plenty to choose from, even in the classical and opera genres and especially in the musical genre). Granted in most cases the song wouldn't be the
exact right length and one would need to make a decision of where to cut it off or how to add 10 seconds of something, but this would be easier than trying to cut a lot of different pieces together and in many cases I truly think no less effective. I even can think of several skaters who have done this effectively recently.
Furthermore, many skaters do try to cut warhorses in new ways every year, sometimes in totally new ways, not just borrowing how other skaters have cut it, though often I will give you that there is similarity- again I could aim several skaters who have done this recently (though many of them, IMO, not as effectively

)