Of course they respond to calls that don't require armed escort, which is why I want them to respond to MORE calls like that (welfare checks, etc.).

The calls you described, they will go to without escorts. If someone, however, calls about a person passed out on a sidewalk or an elderly person missing an appointment, they will NOT respond. If there's a mental health crisis (no weapon), they will NOT respond. That means police are sent, which for many people, is triggering and makes the situation much worse.