Agree with corporal and jaydees comments. There is a difference between hard hands and carrying them with proper alignment. Alignment is functional. Ideally that means NEUTRAL and receptive, and being part of an independent seat. Of course that takes awhile to develop. But the accepted 'rules' of ear/shoulder/hip/heel/straight line from elbow to horses mouth/upper arms hanging vertical help the seat function optimally. These ideas are based upon what I was taught, as well as starting 10-30 horses yearly, as well as many students from beginning to fei. And I also am a judge.
Book are great for thinking out theory, but time riding as well as training and teaching is living in the real world.
There is a vast difference between wide hands per se and 'funneling the horse into a connection. There are reasons for the use of the rein effects, and equally how close the hands are held and why.
Should the less educated rider express training ideals? Ideally they are given time to develop a seat on a lunge before picking up reins. On this side of the pond, it is rather learning equitation while learning how to train their horse. Nevertheless the closer to ideals they are, the more easily the horse will be trained. That said, it is all rather like learning to play chess, learning what action creates what reaction in the horse.
I agree that too many riders do 'hand ride' rather than let the horse meet the hand with steady connection. But low hands often are locked at the withers most often causes either resistance or over flexion. When I was young I also taught what you have stated: low hands/hold a strap/etc., and in the end the riders had much more difficulty in learning a correct upper arm positioning and in identifying the correct seat('s use). In the end the rider must learn the rein effects and a proper posture, each feeds back into the other.
NO one should have their hands to their chest, and should NEVER pull back...the horse meets the rider. That is why the rein effects, and the different rein holds, have always been taught. Those things are not what the pix of Gal/etc show.
When the rider is following the bascule of the horse (in walk, canter, jumping, and seeking forward/down/out/stretching), it is not just the elbow. The elbow allows for an up or down action, or can be opening(taking the upper arm forward). But for opening the shoulder socket must be part of that mechanism.(the same idea of our walking briskly). A very collected horse which is sitting more has need for use of its 'balancing rod' neck, it is more lifted/arced, the bascule is minimal at that point. The action is NOT pumping, it is holding a light connection with the mouth and allowing the horse to use its body. Collection comes after the steady connection, after bit acceptance morphs into the horse being 'on the bit' (with greater degree of longitudinal flexion), and after half halts can produce more flexion of the hindleg joints and a shorter base of support. IF the bascule or the horse is not allowed at the beginning, the use of the neck (in walk and canter) will be restricted. If that happens the horse's natural movement will be restricted, and they will either flex (at the wrong vertebrae) or slow (because of the lack of allowing the body's action).
EVERY rider learns to deal with their own anatomy, tall/short/long waisted/short waisted/etc. But the alignment of their spine is what allows the horse to be ridden 'from the seat'; that has always been required for refinement in riding. Here is a rider which is 5'---on a team--and carries her (shorter) arms vertically Google Image Result for http://equisearch-media.s3.amazonaws.com/wp-content/uploads/2009/02/debbie_mcdonald_brentina_bulletin_400.jpg
Imho its always a refinement of equitation to allow for refinement for (ease in) training.