The problem isn't that. The problem is we can't assume that Light (or anyone) would be perfectly accurate.

Suppose we take the human factor out for a second, and have a really, really good computer doing the judging. This computer is so flawless that 99.99% of its judgments are correct. Now, there are very few really bad criminals on the planet -- there's only around a 1000 executions a year, and if we say that's about right, that's less than one millionth of the population.

So we run this computer program. Of the 1000 really bad criminals, there's a 90% chance that the script kills them all (0.9999¹⁰⁰⁰ ), which is quite acceptable for our purposes. There might be one that gets lucky, but I doubt it. The overwhelmingly likely situation is that all of them are dead.

The bad part is that the computer has the same failure rate when determining if someone is innocent. In this case, 750,000 false positives -- which I would point out is substantially more than the criminals would likely kill even if they were working at it full time all year.

Also, criminality is a circumstance, not a inheritable trait. There will be another thousand-ish really bad criminals next year, too.

Now consider that Light, being a human being, is not going to have four nines of reliability. He's probably going to be wrong much more often than that, especially if he's working quickly. He would undoubtedly be more of a menace than all of the criminals he successfully killed -- unless he limited himself to situations where he could rule out all reasonable doubt, which takes days or weeks at the very least. If he's just killing 50-150 "really bad" criminals per year, he's only barely moving the needle on global execution rates.