Many, many riders focus on the head and neck when schooling. At Elementary levels upwards, a greater element of collection is needed, but a lot of riders forget that their is an entire horse to collect. Their version of "collection", not that it really is that at all, comes from bringing the head and neck up and in. Meanwhile, the back end trails out behind the horse, who hollows their back and drops onto the forehand.
When training a horse, there are a few things that I focus on. Yes, you want a "soft" neck, and a relaxed jaw. A horse that is braced against the hand can't work correctly over their back any more than a horse who's head and neck is crammed in on itself. So yes, suppleness through the body, and the ability to ask for flexion is generally a good thing. What must also be considered is that, to avoid falling flat on their face, the horse must have something under their centre of gravity i.e. the hindlimbs need to be active, and not just tracking up, but coming vertically under the saddle - preferably directly below the rider's centre of gravity too. The back is also crucial, it needs to be strong and lifted.
So, when looking from the ground, in the mirrors, or at a video this is what I look for, in the order that I look;
1. Is the horse tracking up?
2. Is the hindleg coming under the saddle?
3. Is the back lifted? (P.s. look just behind the saddle)
4. Is the horse relaxed in their neck, poll, and jaw?
The head and neck is the least important consideration in my eyes, it's a by-product of a horse that's going well, working correctly, and in good posture. I don't care how "correctly positioned" the head and neck of a horse is, if the other areas of the horse have been neglected. Fixing the head and neck carriage is fairly straightforward, if and only if, the horse is in good self-carriage and/or the basic mechanics are as they should be. Without that, you've got nothing and it's back to square one.
I am a dressage trainer and general equestrian coach in Surrey, Sussex, and Berkshire. I teach dressage lessons, and hold a range of riding and equestrian clinics around the UK, and use my blog to share horse training tips, advice, and resources.