I think like with any other tools they work for some horses and don't for others. The sidepull I used to start my horses with was nothing but a wide leather noseband with the headstall and reins. Almost 0 stopping power of course, but you could control the turns, back up and such. I think it's a great thing to use on quiet horse when you put the beginner on to keep him/her away from the horse's mouth. I don't think though sidepull is a great thing to use to progress in training (probably with the exception of the trail rides).
These side pulls actually have bit to them. A good snap on the nose with them sets just about any horse on their butt. They are not there for stopping but if I need them I am sure of them. I ride with them everywhere including along busy highways.
I just know I have control, I have bite if I need it but if you take the reins up gentley you can apply pressure to the nose setting him back on his hind end, steadying the head, guiding closely where he places his feet.
Again I do find neck reining suffers with them because he doesn't feel the shift of weight of the rein as quickly.
I will alternate back and forth between the bit and side pulls, choosing each for what I want to do that day.
I have had people help me get a saddle on a young guy, use the side pulls and have them hold a young horse for me to get on and then after leading me a few minutes turn me loose, open the gate and off I go into the woods. I find given a hour or so on a totally green horse, alone you can teach him alot in short order and bring him back to the barn quite calm/well wore out maybe
but calm, relaxed and listening.
Like I posted early I only every had one horse run through them and end in a wreck. All others listened fine even though they never were ridden before. They work great for stops and turns on a new horse IF YOU KNOW HOW TO USE THEM.