Some years ago, I was subscribed for The Economist. You needed to call support in order to cancel. Every 3 months I'd do the same ritual: call support; tell them I want to cancel; they offer 50% discount for 3 months sub; I tell them I've reconsidered. Every. Goddamn. Three. Months. And what about all the people who don't know about this? Why can't magazines treat their subscribers... you know... fairly?! Why do I have to be a terrible human being and lie my lay to the actual price?
That changed. It is now possible to unsubscribe through the website (or at least, there is a gui to do that). I did that, but my subscription is active until next January, so we'll see.
Last year, I asked their support to unsubscribe me and rejected all the 50% discount offers. They said, 'sure, bro', and, needless to say, early this year I was hit by a (50% discounted) bill for a yearly subscription.
It's worth pointing out that for this issue in particular (unsubscribing online), different customers may get different experiences, even if they went to unsubscribe at the same time. Some states (notably California, but I believe there are a couple more) have passed legislation in the last few years that requires sellers of subscriptions to make it as easy to cancel as it is to sign up in the first place. NYT was, at least for a while, looking at your billing address to decide whether they'd let you unsubscribe online or not.
An economist would say this is price discrimination, similar to coupons. If you're too busy to hassle with cutting out coupons, you pay regular price. If you really want to pay less, you can save with coupons.
This sounds like roughly what I've been through with Comcast for the last decade, calling every year so they give a not-outrageous price. But quarterly calls does seem a bit more extreme!