You're not missing anything. Bitcoiners like to talk about how fiat is unilaterally awful and only used by imbeciles. The truth is that fiat has conferred certain 'advantages' to its users, at least for a time. One of them has been the ability to mobilize the nation in different ways, including the one you've described. (It goes without saying that the ability to mobilize for endless war is not great for the actual people in those countries.)
Literally nobody knows how the scenario you've described would shake out, because it's never happened, and beyond that it's hard to reason about. In a world where btc had achieved enough success for your scenario to be plausible, what else would be true? What would the larger state of the world be like? Who are these countries trading with? What kind of economic interdependence do they have? Those things would probably have a lot to do with the ultimate fate of these countries.
But yeah, I've thought of this too. It is a massive advantage to the existing power structures to be able to control money, which is why they do it. Historically, it turns to tragedy in the end, as we know. In the meantime, though, total warmaking capacity would seem to be a giant advantage.