Someone who is very experienced with horses and their body language may get good results from trying this. However, when it is presented as something anyone might want to try, I object. For beginners - which includes a lot of folks with years of time around horses - it can be dangerous and it can ruin a horse.
Have you ever seen a Youtube video of someone trying to be like Hempfling or Caroline Resnick? All the ones I've seen are scary. The poor fool is running around with a pissed off horse with nothing but the good nature of most horses preventing her (usually a her) from getting a hoof in the face. It is like watching a beginner trying to ride like a top dressage rider, only without the years of preparation and training first.
It can be bad enough watching a beginner trying to round pen a horse. But round penning is simpler and less likely to result in a dangerous horse than:
"Once you get to the hind end you would run up making any noise and startle the horse (obviously keeping a safe distance). She also uses a grass reed instead of any whips as an extension of your hand (they are very flimsy). As you come up from behind wiggle the stick a little and tap a little in between the legs if needed. You try not to touch the horse though. Most horses will move out of the way."
I'm opposed to most beginners (including myself after 5 1/2 years) trying to train a horse from scratch, unless under careful supervision. I'm very opposed to encouraging people to try a training method that sounds very "Black Stallion / Gandalphy" unless they first have a ton of experience reading horses.
I also object to promoting this as a way "You can transfer immediately to bareback and bridle-less". There is a reason most people who ride bridle-less start with many, many hours of riding WITH a bridle. You lose nothing by starting with a bridle. The OP mentioned Stacy Westfall, but my understanding is that she starts a horse conventionally and works her training up to bridleless.
Conventional training does not result in a robot horse. My 3 horses are all conventionally trained, but none is a robot. The article I read on this particular trainer (and linked to on the woman's website) pushed the idea that bits are cruel and make a horse submit in fear. Her method, she said, made the horse a willing partner. Well, I'm no expert, but I promise you - Mia is a willing partner, or maybe a somewhat reluctant partner for brief moments, but long term, we do not do anything she isn't willing to do. Her 900 lbs trumps my 175. If she decides to shove it in reverse, nothing I do will make her go forward. Mia is not afraid of me. When someone pushes the idea that bits are mean to the horsie and rob the horsie of their spirit, I wave the BS flag!
BTW - one of Hempfling's videos is titled "Keep Your Horse`s Soul". I have a low opinion of anyone who suggests conventional training robs a horse of its soul.