I don't see how creating a unified military is raising barriers in any of those 3 things. In fact, a unified military would break down barriers to those 3 things.
I'm talking globally, not just in Europe.
The world is trending towards supranational organisations at the moment, which will raise tariffs as well as armies. National sovereignty will end up being superseded, and we'll be a world of super-states. Centralisation falls by the wayside when we should be pursuing co-operation. Groups like the Council of Europe would more than suffice.