This may be slightly asbish, but during WWI there was a Supreme court case on the draft, the argument that they brought before the court was it violated the 13th amendment. Now this was WWI, and America wasn't about to drop the draft at that point, so lets say that case doesn't make it to the court. And instead, a very similar argument is made before the supreme court in 1969. ITTL the Court Rules the Vietnam era draft unconsitutional. The man who brought the case doesn't have to go, and the draft is ended, however those already in the service have to complete their term, what does Nixon do?