If psych facilities prevent suicides 50% of the time in the long term, the correlation exists for the 50% where they were unsuccessful. Psych facilities could be wildly successful, and still suicides would be more common with multiple admittances to the facilities.
I’m not saying you are wrong, but I am asking you to consider you could be wrong, before wading into such a dangerous area.
That said, I personally think calling mental health services is only for true emergencies: they are highly toxic environments where a bunch of loonies are locked up together and the nurses and doctors can also be toxic as hell. Putting an 18 year old girl under the power of a 40 year old male psychologist who demands obeisance is deeply sickening. She told me she had been previously committed “for her own safety” (I guess manic sexual behaviour), and she said she was raped while in the facility. Sometimes someone is mental as fuck and committing someone to the psych ward is necessary, but I personally would try all other avenues I could safely do so, even at risk to myself. It is a nasty situation and there usually is lots of downside risks regardless of choices made.