This may get long, may not. But I believe it will shed a little light on the subject.
I believe some are more naturally talented than others to play pool. But, that only gives them a head start on playing very well. It is not a limiting factor. What one has to do, is look at just what "natural talent" actually is. Why can some savants play music so well, or work with numbers beyond what "normal" people can do? Just what is "talent"? Therein lies the answers.
Each of us that has a working brain has wiring connections in that brain that enable us to do things. The wiring of the brain is a certain amount and wired a certain way in our formation in the womb. However, that wiring does not stay that way forever. It is constantly changing every day. That "wiring" is responsible for what we can and cannot accomplish. When someone has a stroke, some of that wiring is destroyed. That's why they can longer speak, or walk, or move their arms, or whatever. Yet, with intense training, most can regain some use of their limbs again.
They do that by repetition. Repetition forces the brain to re-wire itself, make more connections, and work properly again. This process is extremely fast in the young, and decreases with age, but never goes away completely.
Just like men and women's brains are wired differently, which gives them each different "natural" abilities, each of our brains are wired a little differently. The more "connections" one has, the more adept we are at doing something.
When you take a child and train him to play pool, he will learn much faster than an older person will learn. That is because the young rewire the brain much faster than the old. And, it will take far less repetitions to learn something than it will take the older person to learn to do the same thing. Because of that, an older person that had some activity to increase the wiring for hand-eye co-ordination early on will learn to play pool much faster than the older person that never had those activities.
The older person can still achieve the same level of performance, but it will take much more work to do so. At an older level, there is no "realistic" goal to make all that work worthwhile, so it is rare to find an older person actually take the time to train as necessary. So, because it is rare, most say it can't be done. It can be done if the desire is there. Stroke patients are a perfect example of having the desire to work hard enough to re-wire the brain.
Now, the part about becoming a pro player at a later age- yes, that is very possible to happen. However, it also is very unlikely to happen. No reason for anyone to work that hard for it.
One must also take into consideration one of the larger, often overlooked aspects of the game. The mental side of it. The mental side is what largely differentiates the upper levels of play. Just like one has to attain the "wiring" for repeatable fundamentals, one must also almost always rewire the brain for proper mental aspects of playing at a high level.
Because of this wiring of the brain, anyone trying to get better after a few years is best served by using proper fundamentals. Proper fundamentals require the least amount of wiring to be installed. Crooked strokes like Mike Davis for example, require that either one learned early on with faster wiring installation process, or one needs to allow for much longer time for wiring all components to make a stroke like that repeatable. It can be done, at any age. But, it will take much longer to learn than learning the "textbook" way will.That is because there are many more aspects to it, and it requires a much larger amount of wiring all connected correctly to achieve the desired outcome.
The more wiring we have for a given task, the quicker we will be able to "recall" just what to do. The more we know what to do, the more wiring we have. That is why it is so important to really pay attention to details. What does what. That detail orientation is making more wiring for what we want to recall. The less we use a certain wiring path, the more that wiring will diminish until eventually we can't recall what we once knew.
You often hear instructors say to not play competitively for a while after getting a lesson. The reasoning behind that is just what I stated above. In a pressure situation, our mind will revert to the easiest path for remembering what to do. That would be the path with the most wiring. That would be the old way of doing things. It requires repetition of a new way of doing something to create that new wiring path. The more we do it, the more wiring. The less we do the old way, the less wiring in that path. Eventually, the new path becomes the default path, and over time the old way can actually be diminished to the point that we can't remember what it even was. Proper fundamentals require the least amount of wiring to make a solid default path to remember. Hence, it is usually the method taught. When someone like Mike Davis goes to an instructor, he has such a solid wiring path already that works for HIM, that only minor tweaks would be added. Not a whole new way of playing the game. No need to create new wiring to accomplish the same purpose. It's when our present wiring doesn't work properly that new ways are added.
Starting to get off track here, so I will end it here for now.