“If you’re arguing for deterrence, so long as the system worked (killed murderers and kept innocent people alive at some acceptable ratio) imperfect deterrence would still be ok.”
There really isn’t much evidence that death penalties deter much of anything. It certainly didn’t deter Martin Grossman.
And in any case, the secular legal system is biased towards protecting the innocent. It is better to let nine guilty people go free than to convict a single innocent person. In fact even with these safeguards there are numerous cases of people being convicted and given death sentences for crimes they did not permit. And the Torah goes much further than does the secular legal system in trying to avoid unjust death sentences.