However, if a business fails to do so, and the only way they have to cancel your subscription is via, say, a notarized letter, I don't see how you can convince your bank that you tried to unsubscribe unless you have sent such a notarized letter.
Typically, the way it would work is that they would say, "You authorized it," and you would say, "Actually, I didn't authorize that payment. I only authorized the prior payments. I never authorized the subsequent ones because I logged in to their site and attempted to cancel, but they did not provide me with a means to do so."
To which they could say no your initial authorization should also apply to these subsequent charges because that cancellation method is not one we accept. In the past, that defense could work. Your NEW counterargument would be: Sorry, but they cannot rely on and profit from unlawful behavior.
The contract as you signed it might well contain a clause that explicitly says you have to perform arcane rituals to stop the subscription: now you have to have the bank analyze the law in your place of residence on whether the contract itself might be illegal. I do not live in the USA and don't have experience with the credit card dispute system, but I personally doubt that this level of legal analysis would be performed by the bank for your, free of charge even.
I have no doubt that you would win this in court, by the way.
Obviously.