Why is it important to dry your tires before storing them in bags?
I think you are missing the point. You have changed the verbiage of "store your tires dry" to "dry your tires". These are two different things. It's saying your tires should be dry when putting them into bags, meaning no excess oil, lubricants, rubber sealants, or water. In other words, if you've just washed your tires off, let them dry off before you store them in the bags. You may want to towel them off to get the dry faster, but that'd be up to you. Don't put anything extra in the bags with the tires. In fact, some desiccant would probably do the tires good to help prevent dry rot while in the bags.
Here's an article by TireRack.com which has some good advice:
Before storing, use a tire brush to clean each tire with soap and water to remove brake dust, dirt and grime. If the tires are still mounted on wheels, use a wheel brush to clean the wheels with an approved cleaner as well. Dry with a towel and let any remaining moisture thoroughly evaporate.
DO NOT APPLY ANY TIRE DRESSINGS. Tire compounds are formulated to resist ozone cracking or weather checking.
Place each clean and dry tire in its own large, opaque, airtight plastic bag (such as lawn and garden bags) for storing. Avoid allowing any moisture to remain and remove as much air as practical (some drivers even use a vacuum cleaner to draw out as much as possible). Close the bag tightly and tape it shut. This places the tire in its own personal mini-atmosphere to help reduce oil evaporation.
Leaving wet tires or tires soaked with goo in the bags will only exacerbate dry rotting and other things which will degrade your tire faster. The whole idea of putting them in bags is to keep them good for longer periods of time. If you put any of the above "stuff" in with them, you're really defeating the purpose of bagging them in the first place.
I hope this helps your understanding.
Many people have a spare set of winter tires mounted on rims. To reduce the cost many people use less expensive steel wheels. The steel is prone to rust, especially if sealed in an air tight bag with high moisture content and coated with road salt. The other consideration is the potential for mold growth. While in may not be an issue for the tire it could become a health and odor issue when the bag is opened.