Then only accept credit card transactions at the checking desk... I reckon my eventual card transaction much have taken all of a minute to process - about the same length of time the checkin agent had to spend arguing with me about the need to join another long line in order to pay.
Right so therefore you need a card machine at every desk and ensure that the people at the desk know how to use them, then there will be the people who can't find their cards because its in one of their pockets or rucksacks or they forget the pin or it just doesn't seem to want to work while passengers who comply with the T and Cs stand behind waiting and waiting.