I don't see how stats go to the extreme, but I do see how people dismiss stats when they don't understand them or they make them look wrong ( see Avondale Red Rage) or they misuse them because they don't fully understand them, but you don't blame the hammer for the carpenters ineptitude.
Baseball, being a game of situational states and individual performances lends itself to statistical analysis more so than any other team sport.
WAR is about more than batting so yes, I could easily see a situation where you pinch hit Delmon Young (-0.9 WAR in 2012) for Alberto Callaspo (2.9 WAR in 2012). I don't think your projection of what a "stat geek" would or wouldn't do and that you know better than them holds water.
Some people love the stats, some people just love the game, baseball isn't just stats. That being said, baseball is the most statistically tracked sport - by far