Another point to note is that if a horse has a strong dislike of the action of curb bits (like pelhams, for example), they may also react badly to a hackamore since it has, in effect, a curb action without a mouthpiece.
Fin, the stallion I mentioned, was bitted conventionally with a metal bit. He was backed and ridden away with the bit and was already working well in an outline when he went on loan and had his accident. When we first put him in a hackamore he started going heavily on the forehand, because of the "head down" action Lgd describes. It did take a while and lots of leg work to lighten him again - although, as I said, he did end up going very well in it.
To be honest, if a horse was unhappy with a bit I'd be inclined to try a different bit before trying a hackamore - for example, if he was unhappy with a metal bit it might be worth trying a rubber one. This is not to say bits are any better than bitless - but it is worth bearing in mind that just going bitless is not necessarily the solution to the problem.