The anthropic principle solves Harry finding himself in a consistent one nicely. We don't know about the paradoxical universes because time/magic destroys them. You could also propose that when paradox occurs time goes back to the point of paradox and makes changes, inserts prophecies, etc. (maybe even uses mind magic?) to attempt to correct, destroying only the portion of the time-stream that came after. In this version there is actually just one time stream, not many, and it loads from the last checkpoint so to speak whenever a paradox results.

Results like "DO NOT MESS WITH TIME" really imply an outside intelligence that is meddling to ensure consistent outcomes, rather than a universe that runs only on physical law. This isn't a reponse Harry would have thought of, it was inserted from somewhere external.

Regarding "computational difficulty":

1) We don't know what magic/time/the external universe is capable of, computationally. Magic does "impossible" stuff all the time. 2) It doesn't matter how difficult it is to compute or how long it takes. These things are transparent from an inside perspective. 1 second in-world could take a billion years to calculate, and it would still seem seamless from the inside.