When I get takeout, its almost always from places that also do delivery (some of which also have dine-in). If I get delivery, I tip the driver. But if I'm doing takeout, I figure I'm the driver. I assume if they are offering delivery and takeout, they must have someone responsible to deal with those orders. I certainly wouldn't think that someone ordering delivery should need to tip 20% for the driver and another 20% for the food prepper.
I could see how things would feel different if I were ordering from a place that did only dine-in and takeout, with no delivery. It still wouldn't be worth even close to 20% (might as well eat in and let you clean up my mess then!), but I might round up to a convenient number.