Are mental illnesses countable?

I know that the correct phrasing for this sentence is, but I don't know why.

Many of the volunteers had already shown some early signs of mental illness.

Since the illness is unspecified, shouldn't it be illnesses? Mental illnesses can be counted:

This person suffers from two diagnosed mental illnesses.

So why is it we say "early signs of mental illness" as opposed to "illnesses"? We're talking about an unspecified group of people which may or may not have a certain condition or several conditions.

TheFreeDictionary shares a few examples of the word "illnesses" in literature. In several of these examples, they specifically use the term "mental illnesses". Such as this one

Policy limitations for mental illnesses typically limit benefits to 24 months if the disability is "caused or contributed to" by a "mental illness.

"Illness", when used that way, can refer to any kind of illness, or even multiple kinds of illness. Maybe there are some situations where "illnesses" would be correct, but for the most part you'd almost never use it.

I think the reason is that, in this case, "illness" refers the presence of negative symptoms rather than a specific diagnosis. Whether a person is diagnosed with one single disorder, like depression, or multiple separate disorders, like bipolar disorder, borderline personality disorder, and body dysmorphia, you still would describe this person as "suffering from mental illness", not "illnesses". So whether you're referring to a single person with one problem, a single person with several different problems, or multiple people with multiple different problems, you use "illness" as a singular noun.

You fail to understand that a medical term may be used to refer to a category of disease or to a specific type of disease.

In "Many of the volunteers had already shown some early signs of mental illness" the term "illness" is used to refer to a category, but in "This person suffers from two diagnosed mental illnesses" the reference is to specific types.

You might say "The patient is suffering from two different types of cancer", but you would not say "The patient is suffering from two different cancer." However, "The patient is suffering from two different cancers" is valid.