Good solution.
Anything that auto renews ... you should get a prior warning and the ability to cancel within 30 days of receiving your credit card statement.
Any company that won't agree to that is trying to exploit their customers. If the are selling a good product or service ... they don't need to trick their customers into paying for it.
I'd go so far as to say the same for month to month services when they increase the price. The customer should have 60 days to cancel service and get a refund for the price increase.
Actually I'd love it if it would be illegal to just recharge someone's credit card without their direct approval. If they wanted to get around that they'd have to have it processed as a special transaction type ... and your credit card statements would include lists of these recurring payments ... both the amount and the next time you will be billed.
You can contact the credit card company to cancel a deauthorize a recurring payment.
As an added bonus .. force companies to accept deauthorization as a valid method for ending an account. No more waiting on old to end a service!