Psychology, neurology, etc. should consider the soul as an important variable in human behavior, but mostly these fields treat humans as biological automata - helpless products of childhood memories, neurotransmitters, etc. Psychologists are aware of the importance of religious faith to some patients, and certain religious practices such a meditation are promoted, but mostly psychologists believe in medicating people to solve their problems. There is an assumption that any human soul that might exist is not very important.
On the first part of your question ("why do I want to eliminate souls?"), the answer is because there is little evidence that souls exist. In fact the whole idea that humans have souls and coffee mugs do not have souls is somewhat silly from a scientific perspective. A universal soul running through all matter doesn't seem quite as silly. I hope that answers your question.
You are wrong. Psychologists mostly work through therapy. Psychiatrists medicate and even then they go out of their way to exclude enviromental or societal bias.
As such, if a person undergoes delusions or hallucinations that fit cultural or religious criteria, that tends to be excluded as Psychiatric symptoms. (Besides for most psychiatric symptoms, no neurotransmitter or physical component has been found. Even the link between depression and neurotransmitters is suspect, but we tend to keep that inside the medical fraternity)
For instance, I used to work at a Psychiatric hospital where they brought in a Xhosa woman with hallucinations. In the end, after consulting with Sangomas(Xhosa traditional healers), she was discharged to undergo training to become one. The idea of it being physical was left as a diagnosis of exclusion after Religious considerations were first adressed. Only when Religious factors are outside of the norm of the society are they medicalised (I understand if you are unfamiliar with this aspect as you likely have little contact with non-western societies in which these factors tend to be more pronounced).
Another example would be that a Pentecostal that fell on the ground and spoke in tongues would not be considered a psychiatric case, but if you fell down and spoke gibberish, they would stick a syringe of antipsychotics into you in a heartbeat.
There is the Bio-Psycho-Social model of Medicine that brings all enviromental and developmental effects to bear on the Physiology, but this is again treating the creature. The question of the soul does not arise as it is outside the scope of medicine, but doctors send patients to ministers etc. and the same occurs within Psychology and Psychiatry. They don't treat it, so refer those questions on to those that work in that framework. The soul is not ignored, but is not defined in the scope of medicine itself. Religious factors are taken into account and therefore arguably the soul in symptomology as I tried to illustrate above.
No neurologist looks for the soul, not because they don't think it exists, but because it is unscientific to do so (See my above posts for reasoning).
Most Psychiatric institutions have whole corps of chaplains and are frequently affiliated to churches or religious groups.
As to a world soul being more plausible, on what grounds? I would think both are equally plausible and unfalsifiable from a scientific perspective. Not silly from science's viewpoints but untestable and therefore excluded by its methodology. Your wording is very unscientific here.
From a religious perspective, a coffee mug is not a moral agent or entity and therefore less likely to have a soul.
