Yes, in many jurisdictions, including the US, canceling your credit card does not change your obligation to pay. (Imagine buying a $10,000 physical product and the seller forgets to charge until the day after delivery, and you've canceled the card. You're not getting out of that.)
However, there is substantial friction in the American legal system. Of course, if they can find you, they will send a threatening form letter from a lawyer. If you're not experienced with the legal system, this seems scary. But: big whoop.
It costs $5k-20k to fully pursue a contractual claim. Nobody does this for small consumer purchases. (They will send you to collections, if they know your identity, though. But if they don't have good ID, they can't even attach to your credit score.)
Nobody is going to send a subpoena for your $15/mo subscription on a dead credit card.
These concerns are all frivolous and irrelevant for 99% of consumer purchases that charge in the tens of dollars per month.
In the American legal system, it is important to distinguish between what is possible versus what is practical. And exploit that difference whenever you can.