I know, for you it's political. So no amount of reasoning will change your mind. Ranch life is hard. Time is precious, no rancher is going to waste time on an animal that kills their livestock.
They are going to remove the threat and move on. They aren't going to spend money sending it to someplace else, where it will continue to be a problem, they aren't going to keep it in a cage, they aren't going to wait weeks or months for some nice person to come rescue it.
They don't have the time for those nice outcomes.
Your own ordinances that you posted up show that dangerous dogs are a problem in cities. Dogs in Reno are killed all the time in the pound. It is the very rare owner who goes through the time and expense to save them.
So, your complaint against Noem is unjustified.