Because that's the current structure of how we employ social workers.
Which wouldn't be how they'd all be employed if we engaged in a "replace padres with social workers" program.
The God squad indeed only spends a very small portion of their time on the God part, and that's the only part that couldn't be replicated by a non-religious replacement. A friendly face over coffee can currently be a padre, but it can also be a social worker. And there'll be some added benefit that the social worker won't have baggage associated with their religious affiliation that may cause some folks with religious based trauma to want to avoid them.
Why should it be "either-or"? We also don't employ social workers the same way that a great deal of that profession are employed civvy side. Depending on jurisdiction, the qualification to register as and call oneself a "social worker" can be as minimal as a two year college diploma, whereas Social Work Officers need a minimum of a Masters with training and two years experience in "clinical counselling". And, as far as I am aware, all (or most) military chaplains receive additional training in "clinical pastoral counselling", so they are not exactly without skills when assisting soldiers with problems outside the spiritual realm. The same may not necessarily be true with social workers whose client presents with a spiritual dilemma. Just because religiosity has waned over the last few generations, doesn't mean that soldiers/sailors/the other ones (maybe even a minority of) have no need of clergy, maybe the need is even more so when deployed.
There have been a few other threads over the years about the requirement for clergy in uniform. They usually remind me of the dedication of one particular padre of my acquaintance. I never had much interaction with chaplains during my career or even prior to or after; being an Nfld Irish Catholic it is safe to assume that I'm
atheist agnostic have no use for religion at all.
But I have recognized the service that chaplains can provide to serving members, often done in an informal manner and not in structured counselling as would be expected of a clinical social worker. We had a chaplain with us when we deployed to Rwanda in 1994 on OP PASSAGE. He was the individual that most stood out to my mind. No, he didn't save my soul or gather me into the arms of the Lord (he wasn't a miracle worker), we didn't even talk or interact personally that much. There didn't seem to be that much call for the primary duties of his profession; a photo I took of him saying mass showed about six or seven gathered around him, which seemed about his average customers. But I did notice him going about in his quiet manner talking to soldiers. I know from feedback from some of my guys that he helped them.
However, my admiration for him was mostly for his assumption of what was probably the least desirable duty, burying the dead. Early in the mission, the assumption was that patients who died in our facility would be turned over to family or the local authorities for disposal of their remains. It soon became evident that families were often nonexistent or unable to do so and the "local authorities" didn't care. Initially, with the exception of the reburial of the mass grave, the burial of the dead was usually done by pers not engaged in clinical duties. I remember one of the first children to die in our hospital, it was a tiny little thing; we wrapped it in a sheet and put it in a ration box as a makeshift coffin. With another officer, we carried it over to the graveyard site (there had been a couple of previous burials there); the two of us dug the grave and the chaplain who joined us assisted with the digging. He said his prayers and we went back to our usual duties. The digging of graves (and maintenance of the graveyard) was later done by locals hired for the task who worked under the direction of the chaplain, who participated in the internment of every one who died while in our care.
I can't see a social worker assuming the same role.