Eh, I think you're kind of right about skyrocketing suicide rates but I don't think that will be a Gen Z thing, but rather it will happen to the Millennials once they start entering their late 30's, 40's, and early 50's. The Millennials will grow old and disillusioned and many will commit suicide. If anything, the 2010's opioid crisis could be an early warning sign of what's in store for the Millennial generation.
Chances are that the bulk of the Millennial suicide statistic in the 2020's and 2030's will be from former SJW's and other burnouts of a similar demographic (regretful transtrenders and dangerhairs who aged into being depressed cat ladies) with the non-SJW Millennial suicides being either incels or the more "typical" profile of those afflicted with certain forms of mental illness (bipolar disorder, clinical depression, etc.)
In many ways, Millennials in the 2010's are a lot like how the Boomers were in the 1960's and 1970's, but without the strong post-WWII economy that the Boomers inherited.
The Boomer-driven New Left of the 60's and 70's died out when it became overburdened with extremism and many of its adherents growing up and becoming cynical and disillusioned by the beginning of the 1980's. The result was that so many of these Boomers abandoned leftism, either by going neoliberal or defecting to the Religious Right/Neocons in the 80's and early 90's. Hippie to Yuppie, Greed is Good, and all that jazz.
That was the result of the unique economic conditions of the 80's and 90's, which are long gone.
The Great Recession has been over for nearly a decade but it fucked over too many Millennials, both financially and psychologically, leading to the SJW zeitgeist, lower rates of sex and pregnancy, and more rates of living at home.
If anything, Gen Z won't make as many mistakes as the Millennials because not only will they have learned from the mistakes of the past generations, but it's very likely that the Millennial population will be greatly reduced due to higher suicide rates in the near future, along with current health crises such as the opioid epidemic and high rates of obesity.
The main reason why the Boomers did so much damage was because they were both large in number and long-lived. Gen X couldn't compete due to lack of manpower and the Boomers retiring later than every other generation before them (and having higher average incomes as well) so neither Generation X nor the Millennials could get a proper foot in the door in terms of economic and political power.
Gen X was able to recover somewhat when they reached middle age, but again they are outnumbered by both the Baby Boomers and the Millennials.
While the Millennials currently outnumber every other generation right now, they aren't having nearly as many children as either the Boomers or Gen X (in fact, most Gen Z kids have Gen X parents) and they don't have as much spending power as the Boomers did at the same age and while they have more education, most of them have degrees that are worthless, especially in the case of SJW Millennials.
The Boomers have a lot of disproportionate sociopolitical and cultural influence for their age, but I doubt the Millennials will get that chance.
TL;DR-Gen Z will be able to unfuck the current situation because the Boomers will be dead from old age and most of the Millennial SJW's will be dead by their own hand (either from suicide or drug abuse)