People who are suicidal, generally speaking, are usually suffering from extreme stress, depression, anxiety, PTSD and other mental health issues.
Depression stems from an imbalance of serotonin in your brain for whatever reason. Chemical imbalance basically.
With medication, with counselling, with exercise (a natural serotonin booster), with good diet even, you can alleviate these chemical imbalances.
I'm not saying that's true of every mental health condition. Bipolar, for instance, is a tricky one but as far as I know, stabilising that condition requires finding the right medication, alot of trial and error and being consistent with it.
Therefore, it stands to reason, if there are many ways to help alleviate it, they would do everything they can to stop someone carrying such a task out. It's not exactly like you can change your mind after you've done it. They have a duty to protect the public, even the ones who are harming themselves.
Also, as a side note, the implications after are awful. Someone has to deal with finding a body, someone has to deal with seeing someone jump off a bridge, someone has to deal with the inexplicable loss, blame and guilt after that person is gone. Someone in a suicidal frame of mind cannot see the devastation they leave behind. They're so consumed by their state of mind. They don't understand that alot of the time, people develop their own anxiety, depression and PTSD after witnessing something like that. It spreads.