I agree, if you make it your point of focus on just moving your cue straight then regardless of what parts move, if the cue moves straight on all planes it will make for an accurate strike.
The problems come when that is your only point of focus...which making the cue travel level and straight takes quite a bit of focus an will move your attention from other aspects of the game like position and speed control. So you have to at some point focus on what parts are moving so that when practicing you can actually feel the moving parts. If you only have the the hinge joint of the elbow moving then you can put all your focus into the elbow when practicing. If you have the shoulder, elbow and wrist all moving a lot then that's 2 more moving parts to focus on and the timing of all 3 parts becomes more important. For example you have to drop your elbow at a certain point in the stroke to make the cue travel straight.
But, the most important thing is getting the tip to strike the white where you intended and at the angle you intended. If you have an up and down motion like Mika, or a straight back and forth motion like Judd, it doesn't matter.
I cant think of any instructor however that would teach a complete newcomer to stroke like Mika. It is far too complicated to teach a stroke of that style, especially if it is nothing like their natural stroke. First things first, just make that natural stroke a person has more accurate. This can usually be done with minor tweaks. If its naturally like Mika's or Judd's just work with it if it isn't causing too many problems to start with.
I've said it before. I never give any thought to when my elbow drops because I don't consciously make it drop. It just drops when ever it has to or wants to do so in order to keep the cue moving in a straight line.
I never focus on my stroke when playing. It's all about the things you mentioned for pocketing the ball & position like speed, spin, rails etc.
My many moving parts stroke never distracts me from my playing of the game. I never give any of the parts a thought.
I would think that using a stroke that requires a rather precise setup & keeping one's elbow still the whole time would do more of what you're talking about as being a distraction.
I guess we agree but then we get off when you talk about teaching a stroke.
To me...the stick is straight so why not move it straight.
To me...the less moving parts theory is faulty.
I'd never coach baseball, basketball or even golf with the less moving parts line of thought, at least not until I see that the player has trouble with some aspect of the moving parts that is causing them trouble. If that can't be fixed, then that player is playing with a disability when that part is taken out of the action.
I've successfully coached those sports along with football & I was also offered a job teaching tennis when I was 21 years old.
In sports, the use of the wrist & elbows are very important as is the grip on a bat, club, or racket.
I did not teach my own Sons a golf swing that was easy, I taught them an athletically 'correct' golf swing.
In sports, one has to feel things & then just let the subconscious rule that feeling.
At least that's how I see (& feel) things.
Thanks for answering my question.
Like I said, I think we agree but just go off when it comes to the teaching end of it.
Best 2 You & All,
Rick