At my rink the "punchcards" are all in the computer... whether it's public, adult, or freestyle (or even stick/puck) and I think that the class punch cards may be as well (these have your name and basic skills ID, two free public skate passes, and one bring a friend pass, plus a list of the discounts you get being in LTS) because they can be replaced for a small fee, but I think for the most part people are honest and don't try to copy them. Really I think the main advantage of the class cards is to make check-in simpler, since each skater gets a sticker identifying which class they are in.
I remember one of the last summers I worked at our local rink, they had "unlimited" skate pass cards that you could buy for June, July, and August, and they looked SUPER simple to duplicate (just laminated cardstock), but there was a list of who they were sold to, plus the card had the skaters name on it, and it had to be signed by the employee who sold it, so it's not like you could have just printed out a dozen for all of your friends and passed them around.