Debit or Credit Card are a "hook" product for many banks, allowing them to keep up a relationship with customers through their management of current accounts transactions (a dynamic that is only possible in the 4-party model).
To use a general purpose payment cards, customers need an account with a regular cash inflow, so cardholders are more likely to keep their income in current accounts.
Without a debit or credit card attached to their current accounts, cardholders feel less loyalty to their bank.
In the case of credit cards debit cards, the product represents a convenient unsecured lending tool combined with a payment instrument and a channel that enables regular marketing communications.