So?
You’re only using one deck at a time; so you only need to generate 1 bit randomly 226 times — then use that deck.
You’re only using one deck at a time; so you only need to generate 1 bit randomly 226 times — then use that deck.
There are strong monetary incentives to break all kinds of private keys but most of the time they hold pretty well.
(That does sound like a fun optimization challenge: "write a program to fairly shuffle the most decks of cards per second possible.")