For many reasons. They are exceptionally strong with good hard legs. They have good stamina which makes them ideal for endurance or pleasure. They have a natural apptitude for jumping and are bold. Although they often have a long back, they defy this and can turn, spin and jump like any other horse. Their temperament and intelligence makes them ideal horses for beginners. Even young horses have the sense that many people think comes only with age.
All they want to do is please their rider/handler and have fun doing it. Like any horse, they get bored doing the same thing day in day out and because of their versatility, they are great horses to do a variety of things on. This helps keep both horse *and* rider in a better frame of mind. They aren't scatterbrained and are quite good with their concentration and focus.
The hack ring is probably the hardest field for them to break in to. This is because they are a different shape to the TB's who dominate this area. Their shorter legs, longer backs and coarser heads, don't fit in to many peoples "pretty horse" category. Their movement is great and with an experienced and knowledgeable judge, can make it in this area. It goes without saying that they are great dressage horses.
As with any breed, you have to be careful to pick a horse that is suitable for you. Although STB's generally are calm and quiet, there are some who are quite nervy and fiery though these are few and far between. Keep in mind that what may seem to be an evil horse with a bad temperament, may just be one who has been feed too much grain, mis-treated, and not given enough excersize.
Some STB's never stop pacing because it has been bred into them. If you want a horse for dressage, don't get one of these. Trying to make it trot and canter will only frustrate you and the horse and you wont get a happy horse. However, if you are into pleasure or endurance riding, a pacer may be right up your ally because it is a very comfortable gait that can be done down and up hills just as easily as on the flat.