Well, sure, we can set c and G to 1 if we want to, because it makes the math come out easier. But when we do that, we're really picking units where c and G have those values. But if we don't do that, if we stick with MKS or whatever, then c and G have values that have to be measured.

And if you do set c and G to be 1, then you have to use the measured values to know what your units are within that system.

But maybe the problem is with my use of "free". By "free" parameter, I mean one that has to be measured, that isn't determined by the theory.