Yes, the stubble will usually be left behind. Turning it under just takes more time, requires more cost, more machinery and wear, and dries out the soil. In my area, you almost have to plant soybeans into the wheat. Corn typically has a longer growing season. In WI, you are farther north and your season is even shorter.
Most farmers in the midwest grow corn, soybeans, corn, soybeans etc and alternate yearly. Planting corn every year promotes more rootworm, cutworm growth etc and the crop residue can become a problem. Planting soybeans every year adds little to no crop residue to help hold the soil and depletes the plant matter in the soil. Also corn takes much more fertilizer, while soybeans actually adds some nitrogen back to the soil. The rotation of corn and soybeans is a practice that complements each other. I have known some farmers that have gone at least 5 years straight with soybeans but not common.