Every job from those jobs ( medic, firefighter, cop ) have a single mission including doing these things below
Medic: transport the patient to the hospital
Firefighter: put out the fire
Cop: explore the causes of the accident and talk to witnesses
And in your idea you gathered all missions to put them in one mission,
Clearly it would be great.
I thought of this example more as a starting point. The example I gave is, indeed, just putting the existing missions together. What I'm really suggesting is increasing the possibilities of cooperation between the forces. The advantages of completing a joint mission would be increased Job Exp, Score and Money gains.
I believe you want me to suggest new roles or missions for these forces.
Well, for Firefighters, removing endangered citizens from hazardous situations such as fires, car crashes or even finding and rescuing missing people would be a good start. We have many examples from real life situations in which firefighters act.
I have a few other ideas that could maybe help creating new missions. But I'll leave these for another post, since the general recommendation is one suggestion per post.
I hope I have clarified it a bit.