During my two years of training Apollo, I have heard countless well-meant but less-than-helpful comments from observers:
"You need a strong bit"
"You shouldn't ride a green horse bareback"
"You shouldn't ride in just a halter and lead rope"
"You need (insert equipment XYZ here)"
This is not a post for complaining. No indeed. This is simply to illustrate a basic misunderstanding of horse training: stronger or more or fancier equipment is not the answer.
Because when it comes down to it, there are very few training tools or situations where you can force the horse to do anything it does not want to do.
My horse weighs nearly 10 times more than I do, and has twice as many legs. This gives him an indisputable advantage in terms of leverage and strength.
Most basic horse training comes down to tricking the horse into thinking we have an advantage. Stronger bits or certain bridles, for example, can effectively get the point across that not responding to a light cue will result in discomfort. Yet if a horse learns to push back, or spooks and bolts, no amount of pulling on the reins is going to compensate.
It comes down to "ask" versus "tell." You can tell a horse all you want, but if they don't plan on listening, it can be difficult to impossible to enforce. However, if you have trained your horse well, where he looks to you for leadership and trusts you, he'll do anything you ask.
Neck reining versus direct reining is an excellent illustration. With direct reining, you can ask your horse to do something, and you can tell them with more force applied to the mouth and poll by being stronger with the reins (remembering of course that no amount of pulling or harsh bit can compensate for bad training). With neck reining, you cannot really tell them to do anything - touching the neck with the reins to turn is hardly a forceful command! But if they respect you, this is enough.
Adding a saddle will not get more respect from your horse. Adding more equipment can reinforce cues as the horse learns what they mean, but are not necessary.
Tying a horse to a hitching post versus tying a horse to a lawn chair -- what's the difference? We can force the horse to stay put, or we can teach them that when tied they need to stay put.