You are right. The military made a point of pressing charges that would keep the whole eligibility issue out of the question.
That wasn’t because the military was worried about LOSING on the legality of orders to deploy to combat, but because they didn’t want to give Lakin a microphone for him to spew nonsense over. Lakin was going to lose either way. The military chose an approach that robbed Lakin of what he & his idiot supporters wanted: a platform for their nonsense. It was an intelligent and effective move by the prosecutors.
The Democrats largely opposed the Korean War. There were folks then who wanted to avoid deploying based on it being an unconstitutional war. None of them received any sympathy. Nor should Lakin. It isn’t the military’s job to decide those issues. That belongs to Congress.