As a toolmaker for many years, and having drilled 1000s of holes, this is how I did it. To begin w/....a center drill is only used when the workpiece is clamped in a milling machine or radial drill press.
After the hole location is dimpled w/ a center punch, a small drill {1/16} dia is first used because it's limber and and will be pulled over by the dimple. ...but the workpiece should be moved until the drill runs true. The pilot drill size has to be larger than the web of the final drill.,....Fred