The linked article isn't entirely correct. Yes, in smaller counties and towns the 911 call center may be led by the police department but in any city of any meaningful size, the E911 call center is a stand alone department. Sometimes within a wider public safety department but that department usually includes fire in addition to police, and 911 is usually a peer to the police not subordinate
The focus should be on who is dispatched on the types of calls, not the organizational structure, because in most places it's already what you'd expect and not part of the police
There needs to be a force that can be dispatched to these types of calls, just like they know to send the Fire Department if it requires some kind of engineering/rescue but isn't a fire and isn't a medical call