Unless you damage the card when moving it from one box to another by handling it wrongly then changing them around shouldn’t harm it, it will wear away the contacts on the chip on the card (to the extent that you will see shiny trails on the chip and slight marks on the plastic) but you would have to be swapping the card around very often for this wear to ever cause problems.
When the box initialises a new card for the first time it is sending the box serial and card number to Sky to tie them together, when the box initialises a replacement card (when you see the on screen message for only a few seconds) things are different. The box does not call Sky when initialising a replacement card, either the card or box (or both) are set up so when the new card is inserted the new card number is tied to the box. No one seems quite sure about the details of what actually happens, and what is stored on the new card and what is sent over the air to the box in preparation for the replacement card. This only happens when a card is put in a box for the first time, after that it wont be initialised again.
What stops people duplicating a card for use in two boxes is no one can successfully read an entire Sky card then write it to a suitable card. Seemingly the Sky card will self destruct when you try to do this, and if it doesn’t whatever data you get out of it can’t be used.
Edit, beaten to it by a couple of minutes, need to practice touch typing, or just writing neat replies like RolfW's…