"Largely" unfounded doesn't make it unfounded. It's founded, and relevant, and either will be addressed by people acknowledging its genuine existential nature as a threat or, following your baseless dismissal, people will die.
Yes. IMO, we have to be willing to accept errors of both types (under-intervention and over-intervention) in order to design a system that is the most helpful overall.
Some people who call a suicide prevention hotline will go on to kill themself. That by itself is not evidence of a flaw in the hotline or its policies.