Not op, but the number of cards doesn't matter. Only one shuffle can exist at a time, the "number of shuffles" is not a number of natural objects but rather a cardinality of a set. And as we know sets and cardinalities open the gates of hell.

This doesn't mean it's not a "relevant thing to talk about". It just means that these mathematical constructs while useful don't maintain a direct connection to reality, kind of like complex numbers.