I don't think there are any governments that have that policy. For instance, there are complaints when someone gets polonium poisoning, in spite of people thinking it's because of a government. There are complaints about the occupation of Iraq, from governments. And so on.

There are complaints, but polonium poisoning is a tool of a particular government. The perpetrators who carried out the murder did not face justice, they were given shelter by said government, and very likely rewarded for a job well done.

Other governments use drones to bomb people in various countries with impunity.

If a private citizen does any of this sort of murder of their own accord, they go to jail. The difference between government and private citizens is that the former can exempt itself from the consequences of these heinous acts. That is what is meant by the term “monopoly on violence.” [1]

[1] https://en.wikipedia.org/wiki/Monopoly_on_violence

Legal self defense is a thing, at least in my jurisdiction. So I don't think the government has a monopoly on violence.

Also, your opinion on what is murder is arbitrary. All your criticism really is is, "I don't like the definition currently used". That doesn't contain any reason why it should be modified or how or describe any principle.

The fact that governments can circumscribe the killings they do as “not murder” and have regular people believe them is the quintessential expression of the state monopoly on violence.

A monopoly on something doesn’t mean exclusive, 100% godlike control of it. It just means the legitimate provisioning of that thing falls under the authority of one entity. Copyright is a government granted monopoly on the right to copy a creative work but that doesn’t make it impossible for others to make copies, it just makes it illegal.

"The fact that governments can circumscribe the killings they do as “not murder” and have regular people believe them is the quintessential expression of the state monopoly on violence."

A state, and words and concepts, only exist insofar as people believe in them. You're only saying "murder is [defined]", not anything about governments. If you pretend you are making a statement about government or politics, it suggests that somehow a different system could achieve a better and different state. Everyone defining legal killing for themselves is not better or worse, it's a contradiction in terms - an absurdity.