Tire covers will not prevent dry rot although they might help slightly.
I learned about tire dry rot the hard way. I had a spare under my pickup bed that I decided to put into rotation. I bought an identical new tire which went on the rear right side and I put the former spare tire on the rear left side. A few weeks later I had not used the truck but the spare had horrible cracks and had to be discarded.
I discussed this with a couple of tire experts and learned that tires include compounds to delay dry rot which is caused by exposure to air/ozone. In order to activate these chemicals and bring them to the surface, tires need to be run, flexed and warmed up with regular use. After 4 years of storage - not exposed to sunlight - the unused tire had dry rotted and that became evident when I tried to put the tire into use.
Intense sunlight can speed up the dry rot process but tires will also dry rot without exposure to direct sunlight. If you really want to help prevent dry rot for stored tires, you can try Aerospace 303. The tires need to be cleaned and then coated on all sides. Recoating should be done every few months.
