I agree, if we are allowed to make the UUID arbitrarily large (and not be limited to the 128 bits from the "official" UUID algorithm), it should always be possible to set B to a large enough value so that our scheme assigns a unique and finite-sized UUID to every possible state of the system, since all the system's parameters (number of servers, time, etc) should be discrete and finite. I.e. basically make B large enough that 2^B becomes greater than the number of discrete timesteps in our experiment. That's an interesting observation.
Which can be made impossible.
IDs are part of the finite system and don't exist on their own. And the system can perform a finite number of operations both concurrently and in a finite time-interval with some amount of uniqueness distinguishing nodes and other useful properties. Making it possible to always find an id generating algorithm for this system that can never have collisions.