Your contract, and hence obligation to pay, is with the service provide not your bank. Requiring banks to integrate with any company’s subscription terms seems unduly burdensome and impractical.
Having a list of allowed recurring payments for your card is not an impossible requirement. Ability to cancel approval on your side would not be too complicated for the bank and would be very useful even without integration with other side to really cancel the subscription.
That sounds like tortious interference. Or maybe they'd get away with it since technically they're only providing the means for the customer to violate their contract at the click of a button. But anyways, cancelling your payment without cancelling your subscription doesn't actually save you any money unless the service provider chooses to immediately cancel your account in response.
Nonsense. You also have a card holder agreement with the credit card issuer and as you know they can already decide to stop conducting business with a certain merchant. So they absolutely have power in the setup and they extract healthy fees from each transaction.
This is very possible and fits the spirit of recent regulation towards “making it as easy to cancel as it is to sign up”