Your horse needs their head and neck for balance. Shortening the neck often has detrimental effects to the horse’s wellbeing and confidence. Once a horse can lengthen the top line chain, they can bring the neck up into a collected posture by strengthened top line muscles. This is not done by restricting the head and neck, or by tucking the horses’ chin in.
Take a look at horses necks- no rhomboidius can be developed with a contracted neck. This dip in front of the withers is telling. A horse needs a rhomboidius to lift the shoulders.
The first two pictures of the greys show a top line in healthy stretch. The second two show a behind the vertical posture which causes the base of the neck to jam into the shoulders, forcing the weight onto the forelegs. This prevents shoulder lift.
The last two pics show the neck of a horse ridden behind the bridle, lacking rhomboidius development, and another after being ridden in a long, low neck posture for a few months.
And finally, a horse in a very collected posture with the length of the neck preserved.