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.