That is trivially falsified, the prevalence of mental illness is not really related to the acceptance in society (outside of society declaring things to be a mental illness, e.g. homosexuality). For example in Germany the incidence of people missing work days for mental health reasons is
higher in regions with less academic jobs (a milieu which tends to be more open to these topics) and in the formerly socialist parts (where there was a higher tabooization of mental health topics). Similar patterns exist for suicide.
I think I know what you get at, but it is important to differentiate between e.g. someone with social anxiety overcoming their anxiety to take part in society (the good way of "trying to be normal") and someone repressing what should actually be worked on (the bad way, hurting both the person, and, long term, society).
The important point with all things regarding the human mind (education, psychology etc.) is that one strictly can't infer what actually happens from outside observation alone. Let's say there exist two persons, A and B, and both play 6 hours of videogames a day. But person A is a perfectly healthy introvert, while with person B this actually is addictive behaviour concealing mental health problems the person hasn't found the strength to confront yet. It depends on how they feel while playing, and how they feel when not playing.