I recognize that there is a lot of nuance in this topic.
However I don't think that what I am about to say will be very controversial: Psychologists and psychiatrists are professionals who obtain a PhD in a specific field. Their field, education and training relate specifically to understanding the scientific evidence that exists around diseases of the mind, and treating those diseases. The diseases and the treatments are documented in the DSM. So they are at their core, implementers of what is in the DSM, and their approach is fundamentally grounded in the way that orthodox Western medicine is practiced.
Now mental health is a very broad field and you can pursue better mental health in a lot of ways, there are also are a lot of counselors out there who have different backgrounds. But I think the distinction is both significant and valuable - there is the hard science of attempting to treat disease, and that is different from being a life coach. (Well, psychology sometimes struggles to be a hard science and has issues with things like the replicability of studies, but at least the effort is there.)
You might see one or the other based on your individual needs. If you are e.g. severely bipolar and have a high immediate risk for suicide, this is the type of case which may be more likely to end up in the hands of a psychiatrist and very quickly and correctly prescribed a drug intervention. If you have mild PTSD or just want to work on your marriage, perhaps you have the luxury of time and can go talk about life for a few years with a counselor.
Should "the system" include both? To me it is not that black and white. I absolutely think the system should support the former, medical intervention for people suffering serious disease. As afflictions become milder and more about quality of life, support from the system is certainly nice to have but it would be wrong to prioritize resources toward the latter case at the expense of the former.