But this is not specific to psychiatry. The concept of "pathology" or "disease" itself is not easy to define, though it seems that way. The concept of illness is actually more useful. In a way, "pathology" imparts a value judgment on an objective process and so we already are in uncertain murky waters. With "illness" you know you're dealing with human experience.
At the end of the day, all of medicine deals with distress and functionality; that is fundamentally the reason why people seek medical care, regardless of specialty. So imo fundamentally it all comes down to a subjective criterion and psychiatry is not special in that regards.
The difference is that in psychiatry we do not understand what makes people behave in certain ways so we can help people; the scientific basis remains very tenuous. The DSM categories try to make sense of that behavior in "discrete categories" but this does not map up well to the variability we encounter in clinical practice. There may be similar situations in all of medicine where people struggle to define diagnoses and map them to processes in the real world.
It may be possible that it will not be helpful to organize behavior into discrete categories in the first place because there are simply so many factors that are at play and those factors interplay with each other to a certain level of complexity that are quite unique to each individual.
While I do not disagree at all with the notion that all medicine is about functionality and distress, I think it is important to recognize the subset-superset distinction. Not all functionality and distress are usefully addressed by medicine. While it is an empirical question in some sense, I think it would not be hard to sustain the proposition that the extent to which particular functionality and distress are best addressed in a classical medical model is
just to the extent that they share the features I laid out.
The very tenuous grasp we have on mechanism and etiology is exactly what should make us conservative about what we designate as genuine, medical disease entities. I would suggest we limit ourselves to cases where we have a very firm grasp of heredity, course, prognosis, treatment-response, phenomenology, etc. This is how we avoid pathologizing human behavior excessively (you are absolutely right that "pathology" is a loaded term, but that is what we are proclaiming when we say So and So has Such and Such a disorder). Other specialties struggle with this issue as well, as I said above, but there is a continuum of resemblance to the prototypical case I laid out above. And we are mostly at one end.
I think classification and categorization are necessary if we will ever make progress in actual treatment. The natural history at a sufficient level of detail of any medical condition will be strictly speaking unique, as will the precise interaction of risk factors and such. Every cancer will have a specific timeline and combination of mutations, a specific spatiotemporal pattern of spread, etc. But you can extract regularities across cancers and make chemo work. More research on more specific, empirically derived endophenotypes might give us better understanding, but the DSM categories at present are not at all that.
For entities like GAD or MDD, none of the criteria i outlined above are really met. They are just too heterogenous to be useful. Furthermore, symptom checklist definitions that are agree upon by committee genuinely do beg the question of why this pattern of behavior rather than that should count as a disorder. "Well, because those are the criteria for the disorder." "But why are those the criteria?" "Because they are reliable." "But reliable for identifying what?" "The disorder."
You get away with this if you are really picking out uncommon patterns of behavior. If you are in fact describing something most or a large fraction of people go through, well..