[da_chicken]

Nah, it's much easier than that.

The total amount of computer data across all of humanity is less that 1 yottabyte. We're expected to reach 1 yottabyte within the next decade, and will probably do so before 2030. That's all data, everywhere, including nation-states.

The birthday paradox says that you'll reach a 50% chance of at least one collision (as a conservative first order approximation) at the square root of the domain size. sqrt(2^256) is 2^128.

Now, a 256 bit identifier takes up 32 bytes of storage. 2^128 * 32 bytes = 10^16 yottabytes. That's 10 quadrillion yottabytes just to store the keys. And it's even odds whether you'll have a collision or not.

And if the 50% number scares them, well, you'll have a 1% chance of a collision at around... 2^128 * 0.1. Yeah, so you don't reach a 1% over the whole life of the system until you get to a quadrillion yottabytes.

Because you're never getting anywhere near the square root of the size, the chances of any collision occurring are flatly astronomical.