You're confusing the difference between playing pool for fun and playing pool to improve. That 'B' player is at that rating for the last 50 years because they don't have the drive/desire to become better. Obviously if you want to make false statements and forget what your intentions are, then yes it's easy to cut holes into responses. Were you not implying that the two novices both have a desire to become better? Just one has a coach and one doesn't? Or were you trying to imply that the coach will drive the player to become better? And yes, I flat out believe that twenty something has hit more balls than that eternal 'B' player.
Maybe your math needs some work too. It has been posted before that in 10,000 hours of practice, one should reach 'Pro' status in anything. If we break that down, for a million balls in 10,000 hours(36,000,000 seconds), a ball will need to be shot every 36 seconds to get to a million balls. Now that's just pure practice, no competition. Especially no drills. So unless you're brain dead, the motion of putting a ball into a pocket is simple. One will start noticing patterns of when they miss, and take steps to improve. Those steps to improve may require a little instruction, but a full time coach like you suggest is never needed.
Yes, coaching can help improve you faster as they can find a way to explain things so you don't need to spend several hours breaking through a learning curve. But it is absolutely not required in any shape or form. If you have the desire to get better, you will get better. Now if you have the desire, people will take note and try to help you. But these people giving advice are not coaches. So many false assumptions on your part it's hard to take you serious.