I start with a citation from La Gueriniere who is considered the father of dressage, classical master and inventer of shoulder-in:
The shoulders should be slightly thrown back, but they should also remain unconstrained and relaxed.
If you look at pictures and videos of Nuno Oliveira who is considered one of the greatest riding masters of modern times his shoulders look exactly like that "thrown back but... remain unconstrained".

Both these masters consider position of the shoulders is of great importance in order to skillfully control rider's balance and provide effective counterbalance to a horse, especially, during half-halts and transitions. What I have noticed while I studied engravings in La Gueriniere book and pictures and videos of Nuno Oliveira, the rider's shoulders are slightly behind the hip joint. If a vertical line dropped down from the center of a shoulder joint, this line clearly goes behind the hip joint.

You can enlarge the picture on the left to have a better look. If you drop a vertical line from the middle of my shoulder joint the line goes precisely through the middle of my hip joint. However, the overall appearance of my position of that ever so slightly leaning forward. If my shoulders were artificially pulled back I could have been leaning forward and still have correct alignment of shoulders and hips. However, my shoulders are positioned right in the middle without excessive rounding or pulling back and still I appear slightly leaning forward. I think this is exactly why these masters wanted the shoulders to be slightly behind the hips.
Experimenting during my own riding I found out that the position of the shoulders greatly influence how lower back, pelvis and hips react to the horse's movement. Even very slight forward positioning that is not very noticeable changes this dynamic. This means staying just slightly behind the vertical line without excessive leaning backwards, or arching and stiffening of the lower back allows the rider to use his/her body much more effectively. This sets a better base for effective half-halts, downward transitions and overall ability to guide the horse during movement.
This means the common phrase that shoulders and hips must be aligned on a vertical line is not correct. The better description would be rider's shoulders must be slightly behind the hip joints without excessive leaning or tightening. However, if rider has posture problems such as rounded upper or lower back, rounded shoulders it will create difficulty in putting shoulders behind hip joints. In order to do so such rider will have to lean back more than necessary. It is important to make it work for a particular rider including working on proper posture off the horse and developing a better balanced position on the horse with the help of a knowledgeable instructor.

The problem of leaning forward even slightly is inability to effectively prevent a horse:
- from disengaging and wiggling backwards behind the leg
- from dropping on the forehand

The problem of leaning too much backwards is creating an effect of a carpet pulled forward from under rider's feet. Horses end up constantly running away from a rider like that rather than staying under his/her center of gravity. Half-halts/transitions become a game of pulling and holding on. Also, very often riders lean back by simply relaxing too much and sitting back like in a chair. This is a mistake with the same consequences - horses "will be running way" from such riders.

The more complicated work with a horse a rider wants to do the more precise his/her balance must be. Even little discrepancies can prevent a sensitive horse from performing to his full potential. Learn to guide your horse well. Several bulbs went on during last few rides regarding what it means to guide your horse with accuracy and also lightness. Improving position of the shoulders made a huge difference.

Happy riding...