Right. But it's also not the bank (or Visa's) job to act as an arbiter for paying my subscriptions, especially if I'm in dispute with the merchant. If I am advising the bank / issuer that I do not want to authorize these transactions, it's not on them to say "well, we're here to help them continue to be able to authorize them, not for you to keep your money."

That's an issue between me and the merchant. I don't want MY bank acting as an enabler for the merchant over my wishes, with my money.