Thanks for that.
Here, the police are called sometimes as first responders to people feeling suicidal, and they do receive some training in how to deal with those feeling suicidal. In fact there is a police webpage that says to call them if you know someone is feeling suicidal who you cannot help. Perhaps they have this role because NZ police are still seen by many as helpful officials rather than punitive enforcers, and for the most part they fit that image. They also have a webpage with information on missing persons and suicide
Because the system and funding for dealing with the mentally ill is stretched thinly, many who need inpatient care, such as those needing to be monitored 24 hours such as a suicide watch, simply cannot be accommodated, so they do get seen by police when things get to desperate state, and there is no one else available. There is a older article about this problem here.

My upset was not at the police in general, but at those in the police or in the media who do not see mental illness as a real issue, as shown by the journalist who wrote this article, and the police officer quoted in it. Thankfully, this is not everyone.
Interestingly, a lot of responses to that article expressed the same concerns as I had.

Teenidle: because of your background, you may be interested in this story about how a forum moderator in the USA got the police in NZ to contact someone in NZ who was feeling suicidal.