Here, where I live in the western U.S., were on the edge of the Great Plains breadbasket wheat growing area. It produces millions of bushels of wheat and other small grains. Although wet conditions, in and of themselves aren't deleterious to the health of the grain, it does promote the growth and propagation of various fungal infections. These can be controlled, but the cost of chemicals adds to the production of the grains. Chemical control is the first choice, behind correct and timely fertilization.
It's well known, at least here, that the lack of crop rotation adds to the fungal persistence. But the farmer finds himself in a bind, since, all the modern equipment to grow various crops has become so specialized that it's difficult, if not impossible to change the crop he's growing. Wheat and barley have become very profitable so there's little incentive to change crops.
In actuality, you idea of covering the crop would only add to the problem, since the various fungi are somewhat controlled by air circulation... which would be lacking in a covered crop, no? Interesting question, however...