Surely most/all of the patents around the actual inkjet printing function have expired though, right? I had inkjet printers in the mid 00s and if anything I feel like your average inkjet is worse these days.
It would not surprise me if something similar was happening here: HP's current cartridges have at least one piece that is under active patent protection and they don't manufacture any designs that have no patent protection. I don't know enough to state that's the case, but it wouldn't surprise me.
I would be shocked to discover that there are counterfeit print heads out there the same way there are counterfeit STM32 microcontrollers.
Unless the patents have something to do with the shape of the cartridge or they somehow have a patent on "technique to fill printer cartridge with ink" which would not be so surprising.