My first instinct is to agree with everyone else. Read and let read. I read a lot of "heavy" stuff as a kid, and I learned a lot from it.
But just to play devil's advocate . . .
I'm a SFF reader, and I object to things like what I see as harmful trends in sexism and rape-as-titillation in certain types of fantasy. I feel like such tropes are reinforcing institutional attitudes about women that are harmful.
Now, I'm skeptical that the trend of "sick-lit" this article talks about is actually a problem. But I can sort of get why, if some of these books are jumping on a "trend" and are glamorizing things like self-harm or suicide rather than giving them a thoughtful treatment, some people might object to them. Because if the books are poor depictions of this material, they could be contributing to harmful attitudes those people see as problematic. Books do affect us.
Of course I wouldn't advocate any form of censorship, but it's possible there's worthy discussion material here. You know, if the trend exists, and if these books are badly done in ways that reinforce incorrect, harmful ideas. The way the article's written makes me doubt this is anything but a manufactured problem, as the books cited sound like they are thoughtful, but I haven't read any of them, so I can't say.
(Mind you, I have absolutely no objection to well-written fiction about subjects like self-harm or suicide, and I can think of no earthly reason why anyone would have a problem with people writing/reading about a subject like cancer.)