Nice to hear an actual Chaplain's perspective on this issue.
I have an honest question, though, while you are chipping in.
The way you describe and handle the job, what makes your personal faith important to do it?
Well, speaking only for myself... If I was not a person of faith, I would not feel the same pressing need to advocate for other persons of faith, even if they did not share my belief system. I say that, knowing myself, because as a kid, I was a rabid practitioner of my childhood faith, to the point of borderline denigrating others. (Star Trek helped me with that, though!) I feel it is at the core of my calling to help others connect with their spirituality and/or religious practices, even if they don't line up with mine. Thus, I will go out of my way, even to the point of advocating breaking standard rules in order to ensure the personal liberty of a person of faith (or, at times, someone who has no identifiable religious faith but an otherwise strong spiritual or philosophical perspective) has the ability to practice what they believe and deeply hold fast to.
Why do you think it is important, that a person of some kind of spiritual (a pretty undefined term IMO) faith is doing it?
Well, on the one hand, I would argue in favor of someone in touch with their own spirituality (whatever form that might take) but who is trained in both their belief system and in an awareness of its commonalities and differences from other systems.
Further, there is a degree of legal protection involved, when that becomes necessary. As an ordained pastor, I have legal right to officiate at a wedding in my state, and conversations with me are protected in two planes - first, general confidentiality, at a level which no other health care provider can truly promise to maintain, and second, in my tradition, the seal of the confessional, which ensures that anything spoken of to me in the Rite of Reconciliation remains absolutely sealed. Both of these privileges allow people, even non-believers (usually in the former capacity) to speak freely, knowing that the only instance when I can 'tell' on them is when they are intending to immanently do something dangerous to themselves or to someone else.
Finally, in my environment, the clerical collar carries with it a measure of respect. I can help calm down belligerent folks without getting security involved, and often am able to get them to move forward with treatment, discharge, or other plans that nobody else can communicate with patients over.
You said, you keep your own personal belief out of it.
So, if you keep your own faith out of it, someone without faith could do it just as well? Except we would call such a person a counselor or therapist?
I think there is a degree of validity to your conclusion, and I can't dispute that. However, let me clarify something that I, perhaps, did not clearly communicate:
I do not push my religion on people, force people to pray with me, tell them they have to follow my notion of the divine, etc. However, my faith never leaves my side. It is what enables me to do what I do every day. Visiting with a pagan and giving her a cold cup of water when she is hot and thirsty is an act of compassion that is rooted in my understanding of the Christian gospel. I consider because of Christ, and while others who believe in no discernible divinity may do also, I know myself well enough to know that I would be an utterly selfish person if not for my relationship to God in Christ.
It is precisely my faith that impels me towards helping others. Could an atheist/agnostic perform that function? Possibly. Several military bodies in Europe already have humanist chaplains. Either way, I still think the more plausible format would be to have the Chaplain in charge of a specific function on the ship, with Chaplaincy duties performed as needed.
My example would be the Chaplain runs the morgue. S/he is responsible for the reverent care of the deceased until they are buried in space or returned home. S/he handles all affairs related to the deceased, including coordinating letters to family, packing up quarters, monitoring stasis systems, etc. When requested s/he functions in a chaplaincy capacity.
In the chain of command, the Chaplain could work one of two ways: either the Chaplain can be a civilian who works aboard ship (akin to the Royal Navy through World War II) and wears no uniform. (RN chaplains wore a suit and dog collar through at least WWII.) Or, the Chaplain is assigned to medical, is commissioned, and reports to the Chief Medical Officer as his direct commander.