Why is murder illegal?

Because the government has a monopoly on violence.

https://www.britannica.com/topic/state-monopoly-on-violence

But why do they have a monopoly on violence? If no one has a right to life then enforcing that monopoly is pointless.

Holding a monopoly on violence over a particular territory is the fundamental basis of the modern nation state. The state enforces that monopoly primarily to assert and maintain it's own legitimacy.

Why does having unpunished murder hurt the legitimacy of a state if there is no right to life?

Because it's a direct challenge to government authority.

If there is no right to life why does this challenge authority?