I've drilled thousands of holes over the years, in metal, sheet metal, wood, concrete, and plastic. I've used milling machines, drill presses, hand drills and electric drills. I'm not an expert, just experienced. I've sharpened my own twist drills by hand and by using a sharpening jig, which I really like, by the way, since it puts the relief angle on both edges evenly.
I've also figured out that a well placed pilot hole is worth the additional difficulty in all but the least demanding situations, IE rough carpentry. The pilot hole in thicker metals makes the large hole easier to drill as well as locating it accurately. The use of cutting fluids also make the work 10x easier. I've drilled 11/4" holes in steel using a 1/2" drill in a stand, by "creeping up" on the size gradually.
So all this discussion about wobbly holes, practice and run out is a little baffling. The drill chuck and arbor is what it is, and if it's "far out", not much can be done to get a good clean hole in either wood or metal. Also if the material held is in a vise and is not free to self center itself on the pilot hole it may not be as accurate.
BTW to determine the run out visually, a straight piece of drill rod about 6" long or so chucked up will show a deviation at the lower tip if things are "far out"