To answer your question about students pushing for TW policies; this is an issue of self-report coming from the wrong group(s). Professors are not a good source on whether students are pushing for university-wide changes. Their perception is not always reality, or at least not verifiable reality. And there are no schools where students have pushed for or codified a policy that requires TWs. Even hyper-liberal Oberlin backed down from a flexible, non-forceful TW policy that its students asked for, because faculty were unhappy with it on both totally practical and more political grounds(see here: https://www.insidehighered.com/news/2014/04/14/oberlin-backs-down-trigger-warnings-professors-who-teach-sensitive-material).
Student groups and administrators would be the people to ask about the occurence rate on all this — and really, it would be better to look at actual records of petitions and attempts at policy changes than to just ask people to report what they think the situation is at their school. There is no public information regarding any schools’ student bodies pushing for mandatory, restrictive TW policies where profs could be punished for failing to use them. That doesn’t mean some student groups don’t want that, but by and large all the documented, public (and most of them would be public) pushes for TW policies have been basically aware
As for #2 I think (but we do need more detailed data on this) that most professors who report worrying about the implications of TW’s may be misinformed about what TW’s entail, or concerned that requests for TW’s will negatively impact their academic freedom in some way because they don’t want to be told how to do their job. I can’t verify this for sure, but I think faculty bristle at these requests or the idea of them in the same way that they often bristle at disability accommodations — I know it sounds ridiculous, but a lot of professors don’t want to give out extra test taking time, allow students with disabilities to have note-takers or tutors, etc. There is still a really nasty, misplaced sense among a lot of academics that being intellectually rigorous means adhering to a one-size-fits-all education structure, and that any attempt to shift pedagogy is a threat.