I suppose you would, and I print a copy for each vehicle and do just that. So I suppose it doesn't save anything, wallet-wise, but I keep electronic cards for each vehicle just because it's probably easier to find when it's needed than digging through that black abyss of a glove box.

Fuel card I don't carry, but I can picture parent comments having a fuel card attached to their name, but they might drive a different vehicle each work day ("fleet card" tells me it's for work, not personal).