>As far as they're concerned they only have to pay a one-time fee for transferring the received bitcoin to an exchange and selling it there.
Depending on the fee, which atm can be rather high, this can easily be unprofitable or atleast expensive for the card issuer and even card holder.
Whenever the cardholder makes a payment, that payment is processed against the fiat-equivalent that they have with the card issuer; the card is funded by bitcoin you send in yes but it's backed by the currency they converted the bitcoin into the moment you sent it their way.