It really is a very insightful question. Pastoral care of the dying is so very nuanced that there is no cut and dry answer. I have seen someone with no professional training work with people in such a way as to literally channel peace, well-being, and a certitude of eternal life. I have seen professionally trained Pastors and Priests do the same. I have seen the professionally trained really cause distress as have those who lack any training. At the end of the day it really does come down to who and what the dying person needs to be comforted to bring peace and further a sense of well being and with whom to resolve issues that distress.
Let me do say that there is a wealth of knowledge and access to a depth of pastoral experience that professional education affords and simply is not found outside a seminary. Having access to that knowledge base, and keeping one ear open for the Holy Spirit to whisper when and when not to use it, is of immeasurable value. Then of course the old saw is, “Listen, listen, listen,” and not a lot of people have the wherewithal to do that-especially in our crazy hyper-opinionated world!
A final note, I would urge all to refrain from prejudice one or the other. The Christian church, at least, has a very long and esteemed history of honoring the ministries of laity and clergy. The blind clericalism so rampant is really just stupidity cloaked in wise sounding words designed to brings down those who have achieved a goodly education. On the other hand the elitism manifested amongst the educated is simply jealously because others seem more beloved and approachable. To paraphrase and old, old friend, the body has many parts and all of it are useful.