Violet Evergarden isn't sad enough. It highlights how sad things can and do happen, but it gets there by highlighting how happy they needed to be for that to even be troubling in the first place.
Given Violet's own arc through the entire thing, the show overall ends up as a celebration of things that are worth fighting for, and a discomfiting reminder that nobody is guaranteed anything. Much like Violet herself, the story fights to the very end and never gives up.
If it makes anyone want to kill themselves though, they really missed the core of the show. It can also make you want to fight.