My rule is to never kill off a character for pure shock value, which is what your friends seem to want to do? Unless there's some part of the story you want to tell through the suicide of one of your characters (perhaps doing a commentary on the effects of a suicide in a community? Not everything has to be superbly meaningful, but suicide is so often overdramatized as it is. Showing it for what it is - often the tragic passing of a person who feels hopeless - would be much more respectful and refreshing after all the terrible representations of it in the media). Suicide as a theme or event in a story isn't what I'd consider boring if it's done correctly, but if it's put in just for shock value with no bigger purpose to it, I feel that's just not good storytelling? Mental illness and suicide, all of these topics, imo, should be treated with respect and care, because it's both widespread and horribly stigmatized. I think the idea is promising, but the motivation for writing it isn't very good ig?
Ha, I feel like I didn't even answer your question. Basically, between the two choices, it seems you have a much better purpose behind just putting the character through hell and back, since it would cause a lot of character growth for that character. A desire to bring about a certain reaction should be secondary imo. Besides, watching the character literally lose everything is already painful enough, it's just that readers will get the satisfaction of watching that person grow and eventually rise above their circumstances. That is a story I'd much prefer reading than one that ends with a character's death being presented as a way to hurt the audience (tho I definitely understand the draw of killing a character off for drama or to raise the stakes, but if there isn't a good reason to do it, don't do it).
Anyway, it looks like you don't want the character's story to end, so maybe that's a good indication that it should continue. I hope this was helpful and I didn't come off as preachy. Depictions of mental illness in media is something I feel really passionate about lol.