I deal with a lot of mentally-unstable people, and some of them are suicidal.
The thing to realize about suicidal people, is that they can be really dangerous to non-suicidal people.
"I'm not hurting anyone but myself." is a big fat lie.
I have friends that work for the railroad, and train engineers have to deal with folks that suicide by train. It's bad PTSD. In some cases, it may even cause the train to derail, which could injure or kill a lot of others.
Then, there's "suicide by cop." Those people tend to hurt a lot of folks, before they get their wish granted.
Not everyone just wanders off into the desert, or takes a bunch of sleeping pills (by the way, I invite anyone to ask the person that finds one of these "easy" suicides, how they feel about it).
And, then, of course, you have your suicide bombers, but they know what they are doing, and aren't telling themselves the "I'm not hurting anyone but myself." lie.
That's very different from what you describe. Yes, some suicidal people do some very dangerous things that may harm (or risk harm to) others, but in general things that cause harm to others are already going to fall under some criminal statute. Consider someone parking their car on train tracks, potentially derailing it. That act itself would be criminal whether there was an attempted suicide involved or not. The attempted suicide is not the crime (or should not be), in the train/car scenario, it's parking the car on the tracks that creates a crime.
It makes no sense to criminalize attempted suicide except as a way to punish the individual, it does not help them.