@twinklecake
I'm all for a manga about fighting monsters that cause suicides, but linking it to the actual, globally famous suicide crisis of your country really is distasteful.
I'm not super knowledgeable about the exact nature of the relationship between Japanese-culture and mental illness (I am just a mentally-ill weeabo), but I feel like you're evaluating this from a more "Western" perspective. Asian countries in general do not have a good track record with anything mental health related. Talking about it, treating it, et cetera. Japan lags behind the rest of the world in its treatment of depression (using tricyclics, and not SSRIs like everyone else) and there is a lot of stigma.
I tried applying for ESL teaching jobs in Korea (didn't get them, but whatever). Some of my drugs (amphetamines for ADHD) are just flat-out illegal in most parts of Asia. For the anti-depressants you can only get 60 days worth (which is barely even enough time for them to start working) before you have go see a psychiatrist . Also, if you lie on your visa application about not have a medical condition and then try and go get some anti-depressants you might end up in trouble with immigration. Also, if you disclose the mental illness to any of your co-workers (assuming you get into the country all if wrote down some kinda mental illness at all) you'll apparently face ostracization (or some I've been told that work in the area of sending white people to Korea).
I don't think Japan is quite as bad, (but it isn't great). The humorous approach used by the author is a way addressing a subject that people don't really really want to talk about or engage with.
TL;DR: mental health/illness is a thing that people don't want to talk about or even believe in North America. This situation is worse in places like Asia. The MC super cheery demeanor is a way of addressing what is unformattable topic. In conclusion, I don't think it is tasteless.