I use one personally and have found that the use of a hackamore in replacement of a bit eliminates most, if not all problems I have had previously when riding in a bit. Head tossing, rearing, chomping, heavy on the contact...they're all eliminated just by getting rid of the bit, mainly because the horse is relaxed and isn't being distracted by the intense pressure on his jaw. There is a fine line between pressure and pain, and yes, hackamores (especially long shanked mechanical hackamores) put pressure on the nasal bone, but my horse has never reacted to this pressure, but she has RESPONDED to the pressure and is so much more relaxed.
With a bit, I get so many more REACTIONS instead of responses and horses will become tense as a result of unwanted discomfort in the mouth. Many underestimate the sensitivity of a horses mouth and the sharpness of the bars - it is NOT comfortable for anyone!
A hackamore really proves how well you can ride and shows your relationship with your horse. The horse doesn't need a bit - the rider does. Nobody should need to rely on metal to communicate with their horses. Your horse will be much more trusting of you if you ride in a hackamore or bitless alternative, since they will not have to worry about having to tolerate a bit.
It takes away pressure from the bars of the mouth and tongue. Like all tack, some horses prefer them, some horses hate them. The pressure is instead all on the nose and poll, so it's just as dangerous to the horse as other tack if used wrong.