> things go badly pretty quick.

Dealing 2^200 hands, assuming that one hand takes 1ns, is more than ... pretty much any conceivable physical quantity one can think of. (Technically, the heat death of the universe takes longer than that but all card decks will be long gone, having been consumed by black holes.)

This is a long-winded way of saying that cryptography with 2^256 security margin ought to be sufficient for all human-scale applications.