This is why I love Apple's Hide My Email. I use it ALL the time and the unsubscribe button is always there. It's not the most polished interface, but it works perfectly.
Also, for any subscription for which I don't use HME, I will immediately "mark as spam" any minimally-spammy email I get. The ones described in the article would be insta-marked due to the lack of Unsubscribe button.
It’s fantastic, and also lets you track exactly who leaked your email.
Firefox relay also good for this sort of thing.