If every pool player played, straight rail, balkline, 3 cushion billiards, etc. they will become much better players in a shorter time.
It's more than most people realize. Is the table,rails playing, long ,short, or true?
Or going in or out of the diamond, for a kick, bank, etc. Getting close doesn't count.
Making a kick or billiard on the face or coming in the back door is a real thing, precision at its best. Navigating through a lot of traffic is not that easy without math as a check valve.
Try playing rail pool and see how well you play without math. Set up a rack of 8 ball and using only 3 cushions you have to pocket the 8 ball in a corner. You can play it with one or 2 rails.
Play at least 10 games because even a blind squirrel can find a nut.
I compare it to driving. If everyone drove a tractor trailer for a year they would understand the rules of the road and become a better driver, although there are some bad truck drivers.
Play by feel, (learn the math), use all the tools available and put it together.
With a click of a mouse, in the pool hall, or instruction, it's all there and easy to learn.
Without desire and passion to advance your game , you could be dead before you run a rack, or actually get in the money in a small local tourney.
With 1/2 a brain, math knowledge straight stroke, and focus = very good player.
Cue ball knowledge and knowledge in general.
As the saying goes...............Knowledge is power.