My back ground is in three day eventing. As such, I needed horses who were balanced, athletic, bold and knew their own minds and jobs. We are all human, there are always times we miss a stride (more so at lower levels or with new jumpers) and so a horse who is rideable, who learns to help his rider when they miss a stride, and who will jump from a bit deep or a bit far off is much more user friendly than a horse who has to be placed precisely and told when and how to jump every time.
This is still very much the way I will train jumpers. The majority of jumping lessons I teach are gymnastics, poles with fences, and lines. In this way, I teach the horse and rider about judging distances accurately and jumping different angles and lines safely. If courses are an issue, the lesson can be directed that way, but training should start, and go back to, lines, gymnastics and teaching the horse to be quick and see his own way in as well as the rider. If you can step off the curb, walk across the road and step up the other side without falling over, you can see a stride.
A jumping horse needs to keep going forward with impulsion, (energy, not speed) he needs to keep balance, with his hind legs being the engine under him, and he needs to hold straight on a line. If we can help him do those three things, he can take care of the actual jumping. Remember that when you are jumping a course of fences, you may be in the arena trotting or cantering around the arena for 3 minutes, but only about 15 seconds are actually in the air over the fences. The rest of the time, you are riding the horse forward, straight and in balance.