I made a post about this on reddit back before the API thing:

Amazon literally disabled/broke the page for unsubscribing from Prime for several days in the period that I needed to unsubscribe if I were to avoid additional charges. I have screenshots, tried different browsers and different devices and networks, etc.

Absolutely scum shit, no way this was an accident or something, not for multiple days in a row.

I hate the way they push Prime and how hard it is to get off it. I’m still angry at how they tricked me into it, and then I spend the next hour trying to get off it. In the end I removed all my billing info as I’m still not certain I’ve succeeded in quitting it. And I’m still getting “Your prime membership” emails.