"Among other things it depends crucially on an important assumption about the laws of physics: that we ought to be able to understand why they work, not just observe that they do work"
IANAP but,
In assuming that there are discrete laws of physics, we also assume there is a subset of all 'possible' events; events that 'can happen'. (Given a certain arrangement of the universe at T1, there is a set of possible arrangements of the universe at T2).
If we assume finite time, the set of events that will happen is a subset of the set of events that can happen. This is because the set of events that can happen is infinite and the set of events that will happen is finite. If both are infinite, then they are the same set.
Infinite time makes it apparent that all of the events that can happen will happen an infinite number of times, because events that can happen are events that will happen, and an event that can happen is never eliminated from the set of events that can happen by having been an event that will happen.