I don't think so. I think it's current justification is typically framed in the form of 'punishment', and its historical justification was purely religious. And, coincidentally, was at least partially about giving the punished person a fair shot at redemption by punishing them while they were still on earth - which is literal god-appeasement.

Regardless, I think equating capital punishment with ritual sacrifice is a fair judgement. No matter how rational our rituals and systems for killing people seem, there's no reason to suggest that the Aztecs did not feel similarly about their rituals and systems. Law is not supposed to be a science, so it's also not free from cultural relativism, even if you're not a cultural relativist generally.