And that's if you're going completely random and not taking care to try to reduce collisions.
A billion seconds at a billion requests per second is already 2^60 items. You'd only need a few billion seconds to have a 50:50 collision chance with 128 random bits, and even less with a real UUID that only has 122 random bits.
You'd hit 1% odds of collision after less than a decade.
If you actually want to go for a billion years, you need to expand that UUID by 50%.
It depends on how paranoid you need to be.
Or do you mean certain folks intentionally chose substandard implementations for some reason?
UUIDv4 is banned in many high security environments primarily because it is easy for people to screw up in practice and it is difficult to detect when those mistakes are made. 128-bits doesn’t leave much room for mistakes using probabilistic uniqueness.