Yeah, but your starting axiom is wrong. Each unit of Planck time is not a server tick in the universe. It's just false. Literally no serious theoretical physicist thinks that's true. It is a *limit* of a domain of applicability in our theoretical models. Just like the Newtonian limit is a limit of the domain applicability of where Newtonian mechanics breaks down and gives way to quantum mechanics.
You're applying classical thinking to your thought experiment, which is getting you off on the wrong foot in the first sentence.