You think there is zero chance that the ink formulation differs between a color printer versus a black and white printer?

I’m pretty sure the reasoning for color ink cartridges relying on both sets of cartridges is that the “black” cartridge is no longer perfectly black in that configuration.

Ive seen older inkjets share inks cartridges between color and black and white only models. And the only reason you don't see that commonly nnow is because people who use primarily black prints bought laser printers now which are chwaper than in the past.