After playing very casually for decades, and fairly seriously for three+ years now, I think I can contribute to the discussion.
There are definite levels and different skills (and coaching topics) required as one progresses:
Phase 1
At the beginning, fundamentals are key. Alignment, body mechanics, stroking, how to aim, etc. This can be done unilaterally, but it's MUCH faster to have a coach watching and advising. A newbie doesn't want to ingrain poor habits or technique. These are the building blocks. There is *some* attention needed when it comes to the mental aspect (i.e., how to perform in a relaxed, unthinking fashion), but at this point it should not necessarily be the focus, although it should at least be on the periphery since good mental acuity and "grooving" the unconscious actions can accelerate progress. This is the phase where external fundamentals coaching can be extremely beneficial, as can self-directed learning via books and vids. Walk before run.
Phase 2
Fundamentals are getting pretty good. Now the key switches from learning the basics to being able to consistently execute them. One needs to learn how to perform in a variety of settings. Fundamentals break down when stress is present. During this phase, one learns how to summon the unthinking shot, allowing the subconscious to take over. This phase cannot be entered until fundamentals are sound. This phase can also be frustrating, because inconsistency here can either be fundamentals aren't nailed down on a consistent basis, irrespective of mental control, *OR* lack of mental control is causing fundamentals breakdown, chicken/egg. (Let's assume that when I say "mental control", I really mean both mental and emotional control.) This phase can be accelerated by instructors savvy in marrying in the mental game with the physical game. In this phase, an individual can leverage various resources on their own, such as vids and books on mental control. Learning can be accelerated by engaging in stressful situations, such as league play, local tournaments or small stakes wagering.
Phase 3
This is where performance really starts to cook. The variance between floor and ceiling narrows considerably. Fundamentals are usually very sound, and mental control is the variance. THIS is where the variability between poor and great performance is truly and mostly between the ears, mental and emotional control. This phase can be enhanced by learning how to perform under extreme stress, such as large tournament play with very strong competition, or higher-stakes gaming.
At least that's how I see it. I'm a C player. I think I'm somewhere in Phase 2, hopefully about to enter Phase 3. I'm just now starting to marry good fundamentals with the ability to summon "automatic" execution, but I very often break down under stressful situations or those with many distractions.
So, in my mind, the skills required at each phase are pretty different, but inter-related, with the mix of physical/mental control moving from the former to the latter as proficiency increases. So it's not a single absolute one-size-fits-all answer. Which is why the response "You need to gamble" isn't always the right answer.
Lemme know if I'm totally off base here.....