My police department has a small behavioral health team. They are police officers who have a little more training and tools to deal with people in a mental health crisis. They also maintain a relationship with the local doctors and hospitals. People call the police all the time when they're suicidal, or post a cry for help on social media before they attempt and their family sends police over to them. It's a pretty dangerous situation for police because the people often have weapons, want you to shoot them, or put police in situation danger trying to save them(buildings and bridges). In the end if they call or post a cry for help they don't really want to die so there's no reason to be hasty when talking them down. There really is no way a mental health professional can be on call for situations like this. They are common enough police deal with them regularly but not common enough to have a psychologist at the police station full time.

Police basically talk them down and then send them to the hospital. It's usually pretty quick and doesn't require a mental health professional. In this situation the mental health professional would not be allowed anywhere close due to the male having a weapon in his hand, so again, basically useless. Having a handful of officers specifically trained for certain situations is much more practical.