Because the Brits are for all intents and purposes the only ones playing snooker extensively, because they don't dominate the other major cue and stick games (they certainly are not showing up over here and cleaning up at 14.1, one pocket, 9/10 ball, 3 cushion, etc.), and because other countries' participants focus on other activities to a much greater/proportionate extent. Looking at other hand-eye coordination activities that involve more extensive interest (golf and tennis come to mind), the Brits tend not to do even as well as the Australians, let alone Russia and a number of other European countries, And how do they do in other less popular hand-eye coordination activities such as ping pong?
I think you are fooling yourself in looking at a group of good, well-organized British professionals in a small pond (primarily snooker) and extrapolating that to dominance on an apples-to-apples comparison. The good snooker players are to be congratulated on their expertise but they don't dominate cue sports in any meaningful sense of the word outside Britain and the results of other hand-eye coordination activities suggest they would be in the lower echelons on a truly comparable, level playing field.
