RE: Mowing and Corn
If the grass/weeds were waste high last fall, it will likely be waist high next fall. Hardwood (or softwood) brush may not be.
Corn is planted in rows for easier management. Rows allows tractor movement through the field for various fertilizer, herbecide, and pesticide management as well as tilling. Corn planters can delivered plant populations at the desired concentration. All of this will maximize yields while controlling imputs for the farmer.
Having said that, corn can be broadcasted with some success. You will just have to understand that management of broadcasted plots will be more difficult and yields will be decreased. Getting the correct amount of seed down will be difficult. Weeds will be more of a problem and handling them will also be more difficult. However, I would not stop this from planting corn.
Last year for the hell of it, I broadcasted about .75 acre of corn with mix results. I had weed problems (mostly pigweed) and didn't put down enough fertilizer. Some areas, the corn population was too thin and others too thick. I also used feed grade corn not wanting to get too much money involve in this test project. The ear size varied from 4 to 8 inches. Some areas where corn population was too thick, the number of ears were low and size of ears suffered. In areas where corn was thin, the ear size was the largest, but weed competion was the greatest. Overall, for what I put into the plot, I was happy with it. There was some feed and a good bedding area (I jumped bedded deer out of it several times). By December, all the corn was consumed.