Let me take that and make a slightly closer analogy: same story, but instead of the police it's the fire department. There are, after all, fire halls all over the place, and firefighters have vehicles with sirens and lights and the ability to move around quickly, they wear uniforms with stripes on their shoulders, and so on...
But security isn't on the radar for firefighters. Their job is to put out fires, rescue people, and pull the occasional cat out of a tree. That's what they're trained for, that's what they wanted to do when they applied to work in the fire dept., that's what their equipment is designed for, and their organization (in the fire hall and as a whole department) is set up to do. Asking them to start doing security work just because they're around the area doesn't makse sense.
I would dare say that coast guard members have a lot more in common with firefighters than they do with cops.
Okay, I'll try to use your firefighter analogy.
40 years ago, they fought fires and that was it.....they were specialists in that field only. But at some point someone figured out that if they could provide First-Responder Emergency Medical Services that we'd save lives.....and so we forced them to change, to add a new skillset.
Now are they the capable of handling a multi-vehicle pile-up by themselves? No. When a higher-level emergency occurs, the specialist agency intervenes directly (Ambulance and Healthcare Networks). But their ability to provide basic levels of emergency medical makes them exponentially much more useful.
To apply the CCG isolation model you propose to Firefighters would have Firefighters driving by car accidents and other obvious emergencies because "It ain't a fire.....and so we don't touch it."