You're using incorrect language there. It creates a bar where a person has to show "this many symptoms" in order to be diagnosed with a particular illness. This is how modern medicine works and none of us question this model when it comes to physical illness so why should it be different for mental illness ? For example flu-like symptoms alone should not be enough to diagnose someone with the ebola virus or AIDS and the same principle applies to mental illness.
>It creates a fear of being told that your problems aren't really problems, and you're just not dealing with them correctly (regardless of the intent of your original argument).
No. It creates an expectation that one should refrain from automatically assuming that normal human experiences are indicative of mental illness. It's normal for human beings to experience certain problems (such as fatigue, anxiety, trouble sleeping, weight gain/loss, etc) during the course of their life and it doesn't mean they are necessarily sick.
The view that "almost everyone is sick but most people are hiding it out of fear" is a ridiculous notion that is probably being injected into the cultural conversation for commercial reasons and I doubt many people take it seriously.
It's never been more socially acceptable to start taking drugs for mental illness due to the pervasiveness of drug advertising. I think it's easy to make an increasingly strong argument that it's been over-normalized to the point where misdiagnosis is commonplace