This is a good way to go to collections (at least in the US) and have your credit rating harmed. Probably not for .25c but everyone who says just to cancel a card to stop annoying bills is not a good answer.
In general you have a point (eg don't try to "cancel" your gym membership by using a throwaway card), but as long as you have the right to cancel the contract and you notify the business of such (eg certified mail, in the worst case), then you're in the clear. It sounds like AWS support had already been notified, so revoking the payment channel is totally applicable in this scenario.