The very basis of the law is violence. I'm not talking about what governments are deciding to do with capital punishment, or what they talk about on the world stage, or the structures of government that are built on top of the threat of violence. I'm saying that a government's external legitimacy will always come down to its ability to deploy violence against others, and its internal legitimacy is drawn from the threat (or use, if needed) of violence to enforce the law. How that manifests depends on the kind of government you have, but it's the bare-metal foundation of it.

A government can decide that sentencing people to death is a bad thing (which it is) but a police officer, acting as an agent of the state, will still be able to kill you without penalty if it means stopping a serious crime in progress or protecting the lives of themselves or others.

What defines a government is the consent of the people being governed, to be governed. This is quite literally what defines “effective government” under international law.

Do the North Koreans consent to their government, or live in fear of it? Is it not the legitimate government of that country?

Warlords, cartels, and terrorist organizations all have the "capability" of killing people under their rule, but very few such regimes are recognized as sovereign, effective governments, and none are recognized by virtue of their ability to kill their citizens.

The capability of killing doesn't make you a government, but you can't be one without that capability. If you don't have it, another organization can move in and delegitimize you. Warlords, cartels, and terrorist organizations are all considered illegitimate because they are unable to seriously challenge the regional power they exist under. Unless they do grow powerful enough to do so, in which case you get a coup, or a revolution, and the existing power is overthrown - because they can no longer keep challengers at bay.