Perhaps in your climate the stalks break down more than here in MN. Here in spring the stalks are just as fresh and strong as they were in fall with our long winters. The field cultivator would be a rake!
The disk is the proper implement for handling cornstalks. Might take a couple of passes if it is a lighter disk.
A molboard plow is good too, but we don't like those in spring here as it makes lumpy hard ground.