You are basically describing a paramedic. They get there nearly as fast as the police already do. The difference being when the event needs a paramedic due to what happened after the police arrived. Everything already exist, therefore it may be more efficient to simply dispatch an ambulance for any 911 call if enough exist, but that is where they fall short. In my town we have enough, but as the population scales up to bigger cities, I would imagine this would fall behind.

You are basically describing a paramedic. They get there nearly as fast as the police already do. The difference being when the event needs a paramedic due to what happened after after the police arrived. Everything already exist, therefore it may be more efficient to simply dispatch an ambulance for any 911 call if enough exist, but that is where they fall short. In my town we have enough, but as the population scales up to bigger cities, I would imagine this would fall behind.