Hmm

in practice, weak-willed people actually cling to life quite well

He-he... Siv, the key point here is that everyone clings to life by default. Both the weak-willed and the strong-willed. So, all your subsequent arguments are incorrect. As I mentioned in the discussion about politics, I believe that a certain degree of reflection and an attempt to think about oneself are not the least important factors in committing such an act. Obviously, all your "homeless people" in the examples simply lack this factor; they simply don't have the proper level of self-awareness.
One of the most famous suicides is Judas Iscariot. Being one of the twelve apostles, he was probably quite intelligent. There is an opinion that the betrayal was actually his ingenious scheme to launder money: that is, he expected to receive money from the Jewish priests, but Jesus would still not be executed. In the end, we know that things turned out differently. Being a person who was intelligent, but weak, Judas Iscariot chose the path of suicide. He possessed reflection, but did not understand some other things. He realized that he had made a huge mistake, but he preferred not to come to terms with it.
Still, he possessed some determination, there is no doubt about that. He possessed a certain destructive determination. But this is not courage in any sense – courage requires overcoming one's own fears, confidence. Determination, however, is also inherent in weak people in some cases. Determination without courage distinguishes the fact that a person may decide on evil and stupid actions, indulging instincts and base feelings. But following base instincts cannot be called courage, because these are the simplest instincts in one way or another. Even if their execution is associated with some higher-level brain activity. Courage, on the other hand, is pure higher-level activity, because fear is one of the strongest instincts, and courage is aimed at overcoming it.