The point I doubt is that the direct proportion is unique among power laws in needing (or benefiting from) an added constant. Every power law can be expressed as a direct proportion with a suitable change of variables. Does this mean it is suitable to take this approach? Is this how the most accurate mass of the earth and sun really need to be determined? Even if this were so, does this make adding the constant is appropriate for models in intro physics courses when testing the hypothesis and accomplishing the learning the objectives can be done adequately without it?Sure, but why pick that particular model? How do you decide your model needs exactly one improvement, and that this is it?
Even if it were true that "every direct proportion needs an added constant in the analysis" (which I doubt), certainly this is a refinement that may be ignored for most intro physics labs (kinda like neglecting air resistance and other common simplifications.)