I'm glad recent posters have understood the difference between a selfish act and an act with selfish consequences.
Also perhaps it would be helpful to make a distinction between suicide threats and suicide attempts.
Throwing oneself under a train may have traumatic consequences for third parties, but it's a pretty failsafe death method. Someone who tries that definitely wants to be dead when they try it. Ditto jumping off or out of buildings. Overdoses on the other hand often fail, and need a lot of planning/stockpiling that might arouse suspicion. If you're that intent on dying you don't want to be "helped" away from that course of action, or prevented in any way.
A poster upthread talked about teenagers who seem to find suicide glamorous or romantic - publicly planning, discussing or rehearsing elaborate or dramatic exits. Also discussed were people who announce that they will kill themselves for revenge or other reasons. I'd say that those people aren't suicidal precisely. If they attempt suicide they may well use methods with a way out - OD just before someone is due to come home, or ringing 999. This is the classic "cry for help" scenario which of course signifies mental illness of some kind but not necessarily suicidal thoughts.
Unfortunately sometimes "cry for help" attempts succeed. This appears to have happened to a teenage friend of DH's some years ago. She just wasn't found in time.
Finally, I read fairly recently that suicides are fairly common in nice hotels. People give themselves one nice relaxed evening alone, then die safe in the knowledge that they are in the hands of unrelated experts. Still horrible for the cleaner or porter who finds them, but less so than for a grieving, helpless relative.