I do agree that it is a bit wasteful but unfortunately it isn't economical for them to retrieve the partially-used cartridges from cancelled subscriptions, so it is just thrown away. It would be interesting if they offered a "buy out" option. When you cancel the subscription with half an ink cartridge they could sell it to you for half of the price.
If they allowed use of cartridges after the subscription expiry then the system could easily be abused by only subscribing for one month at a time to refill your cartridge then cancelling until you actually used it up. There are workarounds for this like minimum subscription length or blocking people based on address but they have other problems.
The real shady shit is rejecting third-party cartridges, that should be illegal. It's your printer and you should be able to decide what ink you use.