What I meant was it's a private or family issue, the services shouldn't have to know.
I assume the families are (usually) informed in time to make this things known.
Furthermore it would mean they would have to have at least one clergyman of every denomination present to ensure that those rituals and/or rites are carried out. Seeing as there are a great many bases where the troops are sent to, not counting conflict zones, because this can change within the space of a few hours.
How many clergymen would be needed join the armed services to make this come about.
The problem with your solution is a matter of time. Certain religions require certain things to be done within a certain time period after somebody's death.
Take Judaism for example, their beliefs demand that the body is washed, dressed in a plain linen shroud and then buried as soon as possible after death. If you've ever seen news footage of soldiers "returning home", (e.g. horizontally), you'll notice that they're always in coffins by the time they come off the plane. I'm not sure how you think the bodies should be transported back from war zones without having their transition rituals already having happened.
Baha'i believers require that their body be buried within an hour's travel distance of the place they died - so those people, (however few), shouldn't come back at all. But of course, unless you specified your religion and there was an appropriate priest on hand, nobody would know that, would they?
You also seem to overlook the massive importance that religion has amongst a lot of people. To you it's probably just a throwaway idea that you can take or leave and the fact that you're an atheist probably doesn't dominate your thoughts day and night. For those people who are religious, the opposite is true and many "turn to God" in every action of their lives.
And yes, in most units, there are priests, (chaplains), of all kinds of denominations on hand to tend to the spiritual needs of the soldiers under their care. They provide not just reassurance of funeral rites but also a day-to-day connection with the rest of their religious community.
