Sort of. You’re renting the ink, not the printer. If you went to Staples or Amazon and got regular ink for the printer, it would immediately start working again.
If you buy ink from the Instant Ink program, the cartridges are sent to you for far less money than a regular cartridge. They sell page based plans where they make the money back and then new ink just shows up in the mail as you go. HP DRM’s these cartridges to prevent people from skipping out on the subscription and printing normally for wayyyyyyy less up front cost.
HP printers suck. And ink sucks too. So there’s a lot of understandable suckiness. But most of the criticisms about HP’s ink DRM are just people mixing up Instant Ink and regular ink cartridges and getting mad they can’t read instructions.