I think half the problem is the reliance of commanders upon chaplains - who are unavoidably a chimera of church wed to state - as though they are social workers.
Commanders definitely have more of an eye toward the pastoral skills of the chaplain than they do toward the strictly religious ministry.
The issue when it came down to it in federal court decades ago was the right of soldiers fully to practice their faith when placed by their nation in dangerous and/or separated locations. The court actually ruled that the chaplaincy was the best answer to the problem despite any areas where there might be an appearance of conflict between church and state.
If it is a responsibility to provide those soldiers with “beans and bullets,” so that they won’t die, then it’s also a responsibility to provide what they consider a critical need about life after death, should such occur.
My experience and my reading of history says that on the battlefield with death staring them in the face, believers are adamant about fully practicing their faith. I’m not just talking about “let us pray.” They want the full range: worship, prayer, minister, sacraments, funerals, fellowship, bible, teaching, preaching, and even Sunday School.
The person who becomes that religious leader occupies a very powerful position in the minds of those soldiers. It behooves any commander to have the confidence of any religious leader who rises to prominence among warriors. And THEY will have a religious leader, whether officially or unofficially.