This raises a question in my mind, though -- why not just go the distance, and formally make the WDF Zeta Cygni's national military? Many political observers see it as such in a de facto sense, the fine print of its contract allows it to act as such, and Zetan politics seem to be aligned with those of the WDF high command. Even the WDF's contract to support the Federation wouldn't seem to be an issue, unless the Federation was insistent that it not serve to further Zetan interests at the expense of the Federation's (and if that was the case, neither the WDF nor Zeta Cygni would seem to have much reason to participate in the Federation).

Of course, there may be other factors I missed, and the last sentence of the above paragraph might in of itself be sufficient cause...