I would just note that "having a single time-traveler pre-punish one crime is worth some fraction of that utility" doesn't really seem to fit this system, since a single pre-punishment falls well under the 'random noise' threshold so its deterrence effect is effectively zero.

There is no sharp "random noise threshold". A single act has some positive probability of increasing the amount of belief someone assigns to the proposition "crime doesn't pay". Rather the expected value of the change is positive.

(This isn't really a factual disagreement, it just depends on how you interpret "fraction of utility" in a context where one act is useless but, say, a thousand are useful; is the single act's utility zero or k/1000? Personally, I straight-up refuse to treat utility as a scalar quantity.)

That's why I called this an acausal coordination problem.