Just because something else sucks more shouldn't normalize this. NYT (and all other subscription based businesses) should make it easy to unsubscribe online without requiring customer service.
Why would it be fraud? I paid for the service when I used it, if the business makes it impossible to cancel a subscription or makes you go through endless hoops to waste your time, that's on them. After I stop paying for it, they'll just stop providing me the service.
If you signed a contract for X amount of months, then I get it, you have to pay, but I always do month to month at the gym, they still make it impossible to cancel.
The solution to that is, you never give them your real name, address, number, email, etc. It's never verified and Privacy doesn't seem to check your name matches.
I've never been able to cancel any subscription with ease, so nowadays I always use Privacy to get temporary credit cards. When I want the subscription cancelled, I try the provider's website, if it doesn't work, I just cancel the card all together.