As you may have gathered from the responses above, there is more than one reason for using a pilot hole.
One big one is to reduce the amount of force needed for the full size drill. This is probably why you are thinking that they are needed for larger hole sizes and not for smaller ones.
But another big, perhaps even bigger, reason for using a pilot hole is for better accuracy in the location of the final hole. If you punch the location of a hole and then use a large diameter drill, the chisel point on that drill may be bigger than the punch mark and that punch mark will not provide much or even any guidance for starting the drill. In fact, the punch mark, with it's raised edges may even encourage the drill to wander off the desired location while starting the hole. This can happen with manual drills and in drill press work if a firmly mounted vise is not used. Heck a drill can wander off center even in a rigid set-up.
My thinking is that when drilling an initial hole I can count on it to be centered to within the radius of the drill I am using. And once a starter hole is established, a larger drill will follow it fairly faithfully. Thus a 1/2" drill will certainly start a hole withing 1/4" of the marked or punched location. But, for many purposes, that is just too much slop. Now, if I start that hole with a 1/8" drill, then it will be centered to within 1/16" and that is a lot better. And a 1/16" drill will guarantee even more accuracy once it is properly started.
I often use a three step sequence: a very rigid spotting drill (or the very small diameter of a center drill tip) to get the initial location properly fixed. These drills will be well guided by a punch mark. Then a web sized drill to make a path for the final drill to follow. And finally the full diameter drill. Using this procedure for ANY sized hole will give me positional accuracy in the range of just 2 or 3 thousandths. So, I have used a smaller diameter drill with holes from, perhaps 3/32", and up. And I have used spotting drills or center drills for virtually every size hole from, perhaps 1/32", and up. Thus, if I need good accuracy in locating the holes, a sequence of 1/16", 1/8", and finally 1/2" may make a lot of sense. Or 1/16" followed by a final size of 5/32" would also make sense. In short, all sizes of holes.
Of course, if the work does not demand it, then I often skip the smaller sized drills and just hog them out with the full diameter. Again, this applies to all sizes of hole. There is NO real size that separates one technique from another.