I've seen metal ones like that which are used in sewing but they typically crimp onto the backing (fabric) such that it won't rotate. Using these would most likely result in two pieces of cardboard stuck together (no rotation).
If you just use two pieces of cardboard, this is true - but if you use three, then the front and back pieces are held in place and the centre piece is free to rotate. Unless you crimp it really, really hard. ;-)
When I do dials and stuff for PnP, I'll generally use the same hole-punch that I'd use for the haberdashery-rivet kind (or drill it out if the hole is too far from the edge), but then use a plastic screw post (which also gets called a "Chicago Screw" or - somewhat curiously - a "Sex Bolt") that I buy in bulk from a binding supplies company to hold the pieces together. The screw post consists of two parts - one smooth-sided barrel with a flange that the card pieces rotate around, with a screw thread on the inside, and one bolt which screws into the threaded hole in the barrel and secures the card in place. They're more expensive than plastic rivets/grommets, but more flexible and less likely to wear out over time.