Roberto,
I am aware that particle physicists like to work with unity values, as I accessed the following site many years ago when I was examining the concepts of a unity metrology system.
http://superstringtheory.com/unitsa.html
I also am aware that if you would ever want to translate values from one metrology system to another there must be identifiable relationships. We have no trouble in translating values between what you describe as "useful unities", SI to English, etc. In the unitsa.html page the definition of c=1 was defined. The definition was "extracted" using the second and the meter, neither of which have a "natural relationship" with anything else in the universe, just "useful" defined relationships.
The concepts presented in the Universal.pdf article allow one to define a pure mathematical relationship between the speed of light, a unit of time and a unit of distance and you do not have to use the meter or the second. The concept also allows one to translate the value from a unity system to one of convenience, i.e., SI units, which uses the strange circular definition for a second.
If particle physicists wish to work with a unity system structured around earth centric values so be it, but I think it defeats their ultimate objective in finding "natural" relationships between truly universal physical values.
