You’re aware, aren’t you, that a color inkjet that only squirts ink out of the black cartridge is, technically speaking, a black and white inkjet printer? A color inkjet is literally a superset of a black and white one.

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.