Well, if we are going to be so literal about the name, then we have to get Barry Bonds in there now!!
And with regards to All Star games, that oenalizes players from teams that have smaller fan bases. Chaves (again, 38.4 fWAR) lost in all Star game balloting Shea Hillenbrand in 2002. In 2002, Chavez won a Gold Glove and a Silver Slugger, meaning he was regarded as the best hitting 3B and the best fielding 3B. But hey, the fans preferred Hillenbrand over him.
And Hillenbrand was chosen over Chavez again in 2005, a season in which Chavez won another Gold Glove (an award Hillenbrand never won) but lost the Silver Slugger to ARod.
So to sum up:
Eric Chavez - 0 All Star games, 38.4 bWAR
Scott Cooper - 2 All Star games, 6.2 bWAR
Shea Hillenbrand - 2 All Star games, 6.3 bWAR
Not buying into this criterion...