GP is saying "minimum payments + interest already do the things you list as needing late fees for" not "there should be no minimum payments".
I.e. regardless if there are late fees or not: you can't be delinquent on any debt, regardless of label, indefinitely. Also regardless if there are late fees or not: the amount you're delinquent will already increase exponentially more than just the sum of the minimum payments you missed because of interest.
And if the borrower does not pay the minimum monthly payment (% of outstanding balance) several months in a row, that is already sufficient signal to the bank to take further actions, such as sending reminder letters or locking the card. Late fee is not needed for that function.
I.e. regardless if there are late fees or not: you can't be delinquent on any debt, regardless of label, indefinitely. Also regardless if there are late fees or not: the amount you're delinquent will already increase exponentially more than just the sum of the minimum payments you missed because of interest.