In medicine, it's a regular trick to find some new patentable formulation or tweak to switch to manufacturing shortly before the original patents expire, so that you continue to have a patent-protected product.
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.
Mentioned elsewhere in this thread, but the print heads are a very specialized silicon chip with internal microfluidic passages, microscopic heaters, etc. Who else would even make them? The kind of thing you would need millions of dollars to reverse engineer and replicate just to enter the lucrative market of... making inkjet cartridges.
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.
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.