we'd have to come to am agreement on what constitutes a need for therapy, but accidents/mistakes happen, and people die in countries that aren't America, people commit crimes of all sorts; theft, rape, murder, etc. people have childhoods that are less than perfect. PTSD isn't a uniqely American military problem either, nor is it limited to the military of America. Neither is depression. So chances are the need for therapy is universal. Not that therapy necessarily precludes such actions, but it helps in the aftermath.
Therapy requires there to be therapists, and for them to be recognized as a need, and for their expertise to be valued, and it's only in America, with it's patchwork of healthcare insurance, that therapy, as paid for by patients, could really take hold. Other counties have no such system, that individuals are used to paying $x00/session four times a month out of pocket. But in America, since other healthcare's expensive to access, paying for one out of pocket seems like par for the course.
Most countries then simply don't spend the money on therapy, hence fewer therapists. That's not to say those country are poor, just that they have other priorities.
Heck even for good therapy, you need to have those.