There is a huge tendency these days for companies to try to control the things we buy and the way we use them.
The business model goes back to King Camp Gillette, who sold his razors for peanuts and made a fortune from selling the razor blades, at least until other companies made them too.
These days technology makes it feasible to check exactly what is happening to the things they sell.
Car manufacturers install features which they disable unless you pay your monthly subscription.
Have a doorbell with a camera so you can see who is outside? It won't work unless you pay your subscription, or in some cases buy a replacement because the manufacturer has declared the unit "too old", though it was only bought last week.
A treadmill or exercise bike from that company which does a lot of telly ads? Without a valid subscription the brakes are locked on. No pain, no gain, so they make sure that you feel the pain in your wallet.
Mobile phone makers refuse to let you repair their handsets. Of course you can send it off to their "repair centre" for a month to have £30 worth of parts fitted for "only" £600, and it will be returned with all your precious photos destroyed, but these days you are not a "customer", just another stream of revenue. They will do their best to get that broken phone into landfill and sell you a new one.
So it is not surprising that HP (and others) are taking the opportunity to try to increase their revenue. You may need to keep copies of the original ads to fight them. If the ad said "HP recommends HP Inks" or some such, that implies that other inks would work, and they have stolen that advertised feature from you.
