> the police does not show up to a fire or an emergency, why would they?
Because they're trained first-responders, who have medical first aid training, vehicles with lights and sirens to move quickly through traffic, knowledge of the local area to navigate around road closures or ambiguous location descriptions, etc.
There are many situations where multiple sub-specialties of first-responders (police, firefighters, EMT, etc) are useful. The police aren't just showing up to arrest or shoot people, in a functioning society they can and do provide valuable service in assisting injured people, controlling traffic around car accidents, etc.
A common joke with firefighters: the difference between a training exercise and a real fire scene is the lack of law enforcement getting in the way.
> Because they're trained first-responders, who have medical first aid training
In many parts of the US they are only trained to EMR level (if that) which isn't particularly useful. Most fire departments require everyone to be EMT and will often have a paramedic on board. Where I am, police are all EMR and will rarely be dispatched to a medical call (unless there's a threat of violence). They will be dispatched to vehicle accidents for traffic control.
Where I'm from the police all have a larger first aid kit than is the typical home and they also have AEDs. If there is any change a police officer can arrive before the ambulance or fire department then they will dispatch the police there because seconds might be counting.
Yes the ambulance and fire department is better trained for these things. However basic first aid (CPR) and an AED in the hands of someone with basic first aid training often beats the most trained professional who is arrives just a minute later. So dispatches will get whoever can get to the scene first there, as well as the right people.
Yes the police often are in the way in a fire real scene - but that is a lot better than all the bystanders watching the fire in the way instead. However it is hard to see how bad it could be, while easy to see how bad things are.
Because they're trained first-responders, who have medical first aid training, vehicles with lights and sirens to move quickly through traffic, knowledge of the local area to navigate around road closures or ambiguous location descriptions, etc.
There are many situations where multiple sub-specialties of first-responders (police, firefighters, EMT, etc) are useful. The police aren't just showing up to arrest or shoot people, in a functioning society they can and do provide valuable service in assisting injured people, controlling traffic around car accidents, etc.