I think "unsubscribe" should only be offered after a customer has been charged. Before that, it should be "cancel" or "annul".

For instance, if there is a "free trial" period, wait until after that expires, and the customer has been charged, before offering an "unsubscribe".

But aside from the hair-splitting, yes, you are absolutely correct. If I have instant buyer's remorse, I should be able to click it away just as instantly.