From my personal experience...
My horse HATED the Dr Cook's bitless bridle. It made him ANGRY and I had to emergency dismount in the arena. However, I've discovered that he loves the S hackamore. Go figure.
There's many horses at my barn that actively work in a hackamore, and many more than CAN work in a hackamore but their owners are....too cowardly to give it a go. I've done it without incident, though.
It's one of those "it depends" type of things. I think that most horses could eventually go in some kind of hackamore - some will need more training with it than others. Some types will work better than others. I suggest trying to buy one used, and buying one without a bridle, to cut down your costs.