Comment by jonahss

Oh, if you were willing to spend $50 a card, I think you can get them down to the thickness of a credit card.

If you are willing to spend even more, you could bundle the card circuitry with the silicon embedded in the e-ink display already, and there are FPC e-ink displays. So it'd be about half the thickness of a credit card and flexible!

(at that point, we'd need to change the plinth interface, probably go for NFC like people are mentioning in these comments)