It's a sticky wicket, to be sure. It seems like the gateway to a slippery slope, but it also seems like to me there should definitely be a point at which it can be said "this is encouraging people to commit suicide." Does this fall beyond that threshold? Probably. But how do we define that threshold for future reference? Where would, say, the original M*A*S*H movie fall on that scale? Suicide is painless and brings on many changes, it says...
As an interesting note, the lyrics of "Suicide is painless" were written by Robert Altman's (the film director's) 14 year-old son, because Altman Senior wanted to create "the stupidest song ever written" and he found it too difficult to come up with lyrics that were "stupid enough" to fit his vision (apparently, the son was able to come up with the lyrics very quickly). The music was composed by Johnny Mandel, and was not initially intended to be the movie's theme (rather just the Last Supper/Not-Really-Suicide scene) but ended up being a hit (and was subsequently used for the TV show, obviously).
Also, the scene in the movie
M*A*S*H is 100% making fun of the stupidity of the suicide attempt and its motivating cause (and is engineered by friends to help cheer the person back up...which presents different issues with regards to routes to addressing depression, but also, movie from 1970...) In the book, (more similar to the movie than the movie was to the show), a similar scene happens wherein the character is more routinely depressed, and his friends also similarly intervene, though there are helicopter hijinks involved.
All that to say, I think a more interesting comparison would be to the recent-ish release of
Joker, and whether that was glorifying violence in the same manner that
13 Reasons Why romanticizes suicide.
I don't know if putting the series behind an age-lock or paywall would end up heightening the aforementioned Streisand Effect (or just be easily outmaneuvered by savvy teens) but I agree that some steps should be taken by Netflix to acknowledge the potentially injurious nature of the work, particularly in vulnerable (younger) groups.
And Fade, I hope your daughter and family are all doing okay.