NO!!!! There is a considerable difference between a one-off payment and allowing a merchant/service supplier to continue to collect charges in-perpetuity. In terms of cheques, a CCA is more like a cheque which you write once, the recipient banks it, the bank send the cheque back to the recipient who then banks it again every month and there is no way that you can tell the bank "This has been banked enough times, I withdraw my authority for you to pay if it is presented again". What I, and I think a lot of others, would like to see is the equivalent of a Direct Debit, where authority is given for the supplier to charge your account *until further notice*. If Direct Debits work, then CCAs should be able to work in the same way.
The vast majority of internet transactions are one-time payments. With these there is no problem, the merchant can produce (if it is queried) the evidence that the card holder authorised that one single 'point-of-sale' transaction. With CCAs, like with Direct Debits, the merchant should be able to produce evidence that the card holder authorised periodic charges. BUT, as with Direct Debits, the card holder should be able to withdraw that authority at a later date. AFAIK CCAs are not used to spread the cost of goods or services already supplied (ie not for payment in arrears), but are used to pay "in advance" for continuing supply of goods or services. So a prudent supplier will make the periodic charge, and if it is declined would cease supply of the goods/service. As payment is (certainly in my experience) claimed in advance, the card holder would not obtain any goods or services for which they had not paid.