A border is a structure that requires violence to maintain.
> A (successful) state contains violence, in both senses of the word.
(The two meanings of the word “contains” being “includes” and “limits”.)
The Empire State Building takes violence to maintain because without the threat of violence someone might carry away all the rocks. Your local library takes violence to maintain because without the threat of violence someone might burn all the books. Your own life requires violence to maintain, because only the threat of violence from the state prevents someone from killing and eating you.
And we do want to be like that, in theory, because violence cannot be avoided entirely in human interactions, and because violence as a regulated market is more humane than violence as a free market, and because that violence in the former case is mostly abstracted into the bureaucracy. For many people in a modern society the closest they'll ever come to seeing the "violence inherent to the system" is maybe a speeding ticket or misdemeanor jail time.
One problem is that the whole illusion of power a government requires to operate falls apart when this promise isn't kept in practice and a large number of people become aware of this failure through media. Perhaps the news and following public outcries about e.g. police violence in the US serve a (second) purpose.
When that falls apart, and people decide to no longer participate in the fiction that is civil society, things can get ugly.
The equivocation of personal and private property only serves to legitimise a system of rentseekers and landlords.
> violent intruders
Very few of the people crossing the border are themselves "violent".
It's an appropriate word for what happened at several borders, fences that were erected were torn down violently and hundreds of people ran over them. What word would you rather use?
https://www.srf.ch/news/international/fluechtlinge-stuermen-... (this is from a failed attempt)