The last time that U.S. farmers planted so few acres with winter wheat, William Howard Taft was president and the opening salvos of World War I were still five years away.

About 30.8 million acres were planted with winter wheat this season, down 1% from the year before and not much more than the roughly 29.2 million acres that were seeded in 1909, according to the U.S. Department of Agriculture.

Farmers...