The person making the call can't be assumed to be an expert. And in many cases, it might seem serious/freaky in the moment, but be less so to an outside observer.
This sounds like a good way to penalize poor folks and have them avoid using the system altogether, resulting in worse outcomes and higher cost burden on the system when preventable issues aren't dealt with proactively.
I get where you're coming from and agree that preventing frivolous calls is a good aim, I don't know that a fee is the right solution.