Here’s the answer, according to a reader on Virginia Postel’s weblog,
Here’s my theory about why politicians use hand mikes (and I will ignore the obvious phallic implications of the practice). A lavalier mike is fine in two situations: (1) where your words are being recorded for television and not being amplified to the audience, and (2) where your words are being amplified, but only so much that they can be audible in the room. If you try to amplify a lavalier mike too much, you will have a problem with feedback, because the mike is both comparatively far from the source of the sound (the person’s mouth) and, often, omnidirectional, so that it can pick up that sound even if it is jostled or pointed away from the source of the sound.
In contrast, you can hold a unidirectional hand mike close to your mouth, which allows you to then turn the volume down and avoid feedback while still achieving a very high level of amplification of the voice. This works best when you have a noisy crowd (which candidates certainly hope to have at their political rallies). Indeed, you will notice that pop singers who do not use hand mikes in noisy arenas can’t use lavalier mikes, but instead use headset mikes (which look a little silly but which keep the microphone close to the mouth and allow for the volume to be turned down and for unidirectionality). Since headset mikes would make a presidential candidate look like a Martian, hand mikes are the best choice.