No we don't. We use the freshest cuttings we can get, and work with them when they are fresh. Or we store them till we have time to actually do something with them. Often Spring is a busy time with planting and pruning and other chores. Summer is busy with watering, eating, preserving, etc. Often fall and winter are less busy time (especially if you have snow on the ground), so if you have the facilities, fall and winter rooting makes perfect sense. I had hundreds of cuttings from last January still in the frig, and I finally had time in October and November to get them started. They are in the greenhouse and I pot-up a couple dozen every week. Before long, I will to figure out some more space for the newly potted cuttings, but they will have a good head start when it is time to put them outdoor in the spring.
It is usually a matter of doing what you can, when you can with what you have, and making it all work.
Do you have any idea how many people in Minnesota have Winnebagos, basements, and one-cylinder kerosene engines? They have all winter to tinker, clean, paint, accessorize, etc. their engines, and then tour the country in their Winnebagos showing off their pride and joy engines. Starting fig cuttings is not so much different. I actually had time to prep some pix for the website the other evening - first time in months. A couple more weeks and cutting season begins, and then it is pure chaos.