There's been serious examination of this sort of time loop before. See Scott Aaronson's remarks which show that it in fact allows you to solve quickly not just NP problems but also everything in PSPACE (which is noteworthy because we know that P != PSAPCE).

Quick note, P != PSPACE is not in fact proven.

Unrelated addendum: It occurs to me that Harry was able to get the "Do not mess with time" message because his outputs and inputs were insufficiently digital. He considered the possibility of getting nothing, but didn't think to lump in with it the possibility of getting anything outside of the range specified. Why did he get specifically that message, preventing him from noticing the problem is easily fixable? Because this is CS world, of course, so we assume that nature chooses adversarially...