There are many different levels of fundamentals, I've experimented with several throughout my career. However, when I found out what all the champion players were doing I took 2 weeks and changed how my body connected so I could go down on each shot the same way and with the ideal perception. From my personal experience teaching thousands of students privately and by video/article I can safely say that almost all players that aren't at the championship level are out of alignment when getting ready to go down on the cue ball to shoot.
This alignment issue will put a demand of 60%-70% (that its probably conservative) of their subconscious mental "horsepower" and under pressure it will usually fall apart, especially playing an accomplished player. I have a lot of success teaching this technique as the foundation of what it takes to be a World Class competitor - all it takes is the willingness to change and desire to practice it for up to two weeks (an hour a day is plenty).
The Game is the Teacher
The upper body is the key to proper alignment.
The lower body needs to morph to adjust to the equipment and other demands that might arise to keep the upper body delivery system in place.
The role of the standard stance, as presented in instruction, is to help us find that alignment slot.
That acts as a reference once established.
I use a simple sheet of paper to help illustrate that alignment.
Set it in portrait mode in front of you.
Take the lower left corner and move it diagonally up and towards the right edge of the paper.
The bottom edge of the paper needs to be aligned to the right edge as the paper starts to fold.
Precisely aligning the bottom and right side edges and smoothing the paper creates a diagonal crease.
The crease is the object lesson.
With the crease anywhere else the right sides don’t align.
The paper represents the body with the alignment opposite the right side.
The hips represent the bottom edge, square to the alignment line.
The body folds along the hip line if you bend from the joints not the waist, our crease line.
When the left foot or knee are moved forward it changes the hip line as it rotates in a clockwise direction.
As the crease created by folding along the hip line, the bridge hand can be reached over to the right edge, the shot alignment.
When the hip plane is right the fold aligns naturally and the body can fold flat.
If the left foot is too far ahead, the flattened back will push the alignment too far right or not be able to get right down fully.
If the left foot stays back square and doesn’t advance, the hips folding forward, make it hard to get and keep the heads position over the shot line.
The hands can adjust that right side alignment somewhat but the flat back plane constrains the variability.
Idealists would find the alignment of the aim line, the cue, the upper arm positioned behind the head’s aim perspective, with a vertical cueing arm, and body right down, the gold standard.
This process can place the body there.
Once the body finds the proper position for the upper body, muscle memory can bookmark that slot.
This process was just to find that unencumbered reference, to start from.
The rest is the ability to morph the lower body including the hip line and still retain the aim and delivery alignment.
And, you are so right, about how that puts attentional demands on the player mentally.
Add the pressure of coping with competitive stress and the fabric of the alignment can unravel under pressure.
That is why a trigger like the folded hip line position can reduce the thought process to a straight delivery from an aligned position.