I think it is a mistake to underestimate the physicality of pool. While it is not an aerobic activity, and can be accomplished by people with many body types, it still requires physical strength and stamina to play at a consistent high level. Much of the stamina is required of small muscles, but it is required nonetheless.
Simply holding the head in position is physically demanding. Holding the stick steady and establishing and maintaining a firm bridge are physically demanding. Don't believe me? Get into a pool shooting stance and try to hold it for 5 minutes. Then think about how long pool matches go on, and how many times you are getting into those positions, holding it for a few seconds, and then keeping your entire body still while completing a smooth, straight stroke without wavering a millimeter.
The deterioration of the game in golf is actually greater tee to green than in putting, as shown in the analysis of PGA tour players in the chart. Interestingly, there is a slight increase in scrambling ability among golfers. The speculation from the researcher who published the following chart is as follows: "Short game play involves a lot of technical skill – stance, position of hands, correct judgement of swing speed, club head position, etc. (in addition to strategy) – while not involving much of the physical strength that declines with age. "
I find this interesting when thinking about pool. Older players seem to be drawn to and compete better in "One Pocket", perhaps because of acquired technical understanding of the game and improved tactical skills.
I hate to bring up a can of worms but there are physiological and biochemical reasons that explain why very few professional woman golfers or pool players are able to compete against young men, and why very few men over 50 can compete against young men.