The problem with that is that legally, the contract to pay a provider, and the instruction to your credit-card company to pay a recurring amount, are two separate things. Some companies will send threatening letters, dept collectors etc after you if you just cancel the CC instruction.

It's different on the apple store, where Apple forced providers to agree that a subscription could be unilaterally cancelled via the store. Ideally we would pass a law so that credit cancellation also cancels a contract as long as the minimum period is over. Not holding my breath though.