I think there's a bit of overemphasis in the article and this discussion on "trigger warnings", as though they're some new phenomenon. They certainly aren't, though the label may be - people have been forewarning that there may be objectionable or shocking content in something they present for ages, and is absolutely both courteous and expected. That said, I think it is extensively obvious that the demand for such warnings can be used as a means of silencing speech that individuals find offensive or objectionable, rather than as a mechanism by which to manage individual shortcomings in one's mental health. It is unfortunate that the term "trigger warning" has become so polarizing, because the concept is absolutely valid and necessary.
One of the co-authors of the article is a professor and social psychologist, and a number of the people cited in the article are likewise college professors who are in the thick of this on a daily basis. I absolutely don't think that it's a majority of people screaming for trigger warnings as a means of censorship, but if there's anyone qualified to opine on shifts in attitude among student bodies and university leadership, I do think it's probably these professors. The argument that "I haven't seen it, so it doesn't exist" is rather empty. There are empirical examples of action taken at administrative levels to codify these kinds of abuses, which is far more concerning than a few students' complaints, because it signals a shift in university leadership towards a direction that can only leave students unprepared to deal with a free society.
Stepping back from the "trigger warning" issue a bit, the greater overarching issue, I think, is the expectation that people shouldn't have to be exposed to ideas they don't like. Claims of mental trauma are one way to shut down discourse, and such a claim is practically unassailable. As such, it is an exceptionally potent weapon for those who wish to manipulate their environment to suit their preferences. None of this is surprising - there have always been people that sought to control discourse to limit it to territory that they are comfortable in - but it seems that there has been a change in the direction of response to it. Historically the onus has lain on the affected person to take action to remove themselves from circumstances that might prove to be overwhelming or uncontrollably distressing, and a forewarning that difficult, offensive, or objectionable content will be presented or discussed is the opportunity to take that action. However, the actions being taken at administrative levels are shifting this responsibility from the individual to the school, to avoid presenting content that may potentially be distressing. This is ruinous in many ways, but most notably, in that it requires the denial of reality.
For example, the topic of rape may indeed cause extreme discomfort to many and even invoke symptoms of PTSD in victims of it. But, refusing to discuss it is not going to make it go away. Pretending it doesn't exist doesn't fix the issue. Suk's article on the pushback to teaching rape law in criminal law courses is exemplary of this; a student in a criminal law class must surely expect that criminal behaviors which exist in our society will be discussed, including behaviors as ugly and traumatizing as rape. To demand that such things not be taught because acknowledgement or reminder of the existence of rape is distressing is an inversion of priorities; to prioritize one's own mental comfort over an education in the realities of the world (which is given, ostensibly, to improve those realities) is to proclaim that individual emotional wellbeing is more important than education and maturation of the mind in preparation for participation in greater society.
Methods and actions which, in good faith, seek to improve mental health are unquestionably good. The mistake, I think, is to elevate them to the most important goal in a setting like higher education. Even in good faith, such an elevation can easily subvert the primary purpose of higher education - that is, the preparation of the student's mind for powerful and effective participation in their community, economy, and society. Applied in bad faith towards the end of political control, it is even more destructive.