If you think that's bad, 5 years ago you had to call someone on the phone to cancel NYT subscriptions (the boiler room retention script always gave you an option to extend at the cheaper rate, but it was a pain to have to go through the motions). IIRC new consumer laws at the state or local level ended that practice.
I'm still paying the NYT intro rate ($4 a month billed annually) and on day 364 go to the account page to cancel my subscription before it resets to the "official" rate. Sure enough, they let you stay at the cheap rate if you tell them you'll walk.
Works for telcos and Adobe, too.
As for alerts and notices you can't unsubscribe from: filter or spam.