The ink is only valid during your subscription period, like most other service subscriptions. When you cancel your phone, you don't to use the excess minutes. When you cancel your insurance, you don't get to make a claim for an event after the expiration date. It's 10 pages a month (or whatever plan you sign up for), so you didn't print and the month is done, so is your ink. You can put in a regular cartridge if you want regular rules, but $1/month to maybe print and they'll send more ink when it dries up seems like an ok deal to me? (Was better when it was free, but they got bills, I guess)
Frankly, I don't expect ink cartridges to work after a month or two if I haven't printed anything, either. I'm happy with the color laser I got from CDW Outlet, but while discounted, it was still probably the cost of 4 inkjets and I don't know if I'll really use it enough to justify. But other than some duplexing oddities sometimes, it just works and that's really nice.