New printers often come with a trial of the manufacturer's subscription plan, which will automatically order ink when it's running low. I guess if you activate the subscription when it runs low, it will send a new cartridge straight away. This probably also works with a real card number if you just cancel the subscription before it starts charging.

I'd assume that only works once per printer - or at least it's enough of a pain to repeat it that most people would rather pay. The smallest subscription plans are pretty cheap.