I never understood the strategy behind the stymie. It is one thing to end up blocking an opponent's shot and another to do it purposely. If you are that good to block another why not just go ahead and make it? What am I missing?
Playing a Stymie is typically a last ditch defensive strategy. If player A is outside of player B and is laying one more, playing a Stymie can help to salvage a half.
I don't recall every seeing a player who was putting for birdie trying to leave a Stymie as a primary play, it's always the player trying to make a long par or bogey putt that may choose this strategy, or looking at a possible Stymie on a through line of a putt after it passes the hole.
To be effective the ball does not need to sit exactly on another players line, being in the near area of ones line is enough to influence another players execution. So you don't need to be as precise as holing a putt, especially when the putt is out of normal make range.