>If money could buy happiness, they there would be zero cases of rich people killing themselves.
Man that analysis is just incredibly faulty. As far as you know they killed themselves months or years later than they otherwise would have. I have way more experience with suicide than I would prefer and can tell you that money troubles are a SIGNIFICANT factor for suicidal ideation and attempts [1].
[1] Wang, Y., Sareen, J., Afifi, T. O., Bolton, S. L., Johnson., E. A. (2012). Recent stressful life events and suicide attempt. Psychiatric Annals, 42.3, 101-108.