War was prevalent in primitive societies as well, it hardly appeared with currency. Currency and in a more general way, an organized society makes you better at waging war, hence their success. If anything primitive societies' wars were bloodier compared to the population base. As for crime and law enforcement, it's the same, people have killed for some gold or cows since eons.

I still fail to see how bitcoins would let us get rid of either crime or war, nor downsize the army or LEOs. Same for the "conventional power politics", it's hardly a new thing, put a 100 random people on a island and you'll see the same mechanisms at play.