killick, in the best of all worlds you are right, you don't fold sails. You do like the racers with high tech sails and roll them.
But in our world, you take the jib hailyard forward with you, and lower the jib while you work up the leech, flaking it as the sail comes down. When you are done it is flaked on deck against one of the rails, and all you need to do it tie it.
If you have the luxury of time and space and hands, you can unhank it and then roll it up into a sausage, then stow that below or against the rail. If you're planning to leave it hanked on or to be able to hank it back on in a hurry, you leave it flaked, and just don't squeeze too tight on the folds.
Everything is a compromise.