Is is really the case that the enroute charges are for some kind of service provided?
If that was so, the charge could not be enforced if the pilot didn't receive a service - simple as that.
I suspect there is no pretence of providing a service. The charge is just a tax on the flight, and can be collected regardless.
The answer, as most twin owners know, is to fly "VFR"
This can lead to some ridiculous practices but what does one expect?