Why, then, does every online store in the world refuse to let you type in those spaces when you enter your credit card number? It's so easy to verify that you typed the right thing when you compare one grouping at a time, and incredibly annoying to have to verify the whole thing as one long number.
I suspect it's just another case of programmers writing for computers instead of humans, but the consistency amazes me. Has no-one looked at a credit card and thought "Hey, there's a usability feature! I think they're on to something here!".