Consumers use credit and debit cards for all online transactions. Such payments, irrespective of the security debate, are not profitable for low values ("micropayments"). We have a similar problem in offline payment, where low-value transactions are discouraged.
Credit and debit card payment incurs per-transaction overhead costs related to authorization, processing, reporting, and data communications. Such fixed costs are independent of the amount of the transaction, and are normally covered by the fees collected from merchants and/or cardholders.