I should be able to tell my credit card company that I'm ending a subscription, and have them be in charge of notifying the provider that the subscription has been terminated
You don't have such contracts with recurring payment products.
For example, Planet Fitness has “no commitment” memberships, but you still have to explicitly cancel.
> You may cancel according to our policy: Per the agreement, in order to cancel a membership, one must either go to your home club in person to fill out a cancellation form, or send a letter (preferably via certified mail) to the club, requesting cancellation. Please note: Memberships cannot be cancelled via fax, phone, or email.
https://www.reddit.com/r/personalfinance/comments/51m0e0/com...