While it is true that there needs to be a nationally coordinated armed forces - the actual bodies should be paid for by individual AEER's who maintain both reserve and full time personnal at their expense (and at their local rates of pay).
Since richer AEER's can afford this and more stressed ones may not be able to - the burden may not in fact be shared equally, bu that's true for a lot of both the costs and benefits of any system of governance.