I actually don't think that's nonsense, because HP is charging per page, not per ink cartridge. You don't get a new ink cartridge every month, you get the ability to print more pages, and only new cartridges as required to print those pages. Put another way, OP's subscription only paid for a fraction of their ink cartridge, not the whole cartridge.
HP could make OP mail back their half-empty cartridge, but that likely would raise the overall cost of the service due to shipping logistics.
I agree the whole concept of this service feels scummy and I would never recommend it to anyone, I just don't find this particular aspect so unfair.