IMO the problem isn't the consent because your latter point that someone using this is somewhat implicitly consenting to help save their life.

It's that "emergency services" is a euphemism for "the cops, who might harm, kill, or traumatize the person or anyone else who happens to be nearby." I know someone who had police guns drawn on them and was ultimately tazed and arrested because of their roommate's call to a hotline.

Extremely dangerous situation. It's not the fault of the hotline that police exist, but they do exist and so it needs to be considered carefully. Cops are one of the most dangerous things you could possibly expose someone in a mental health crisis to.