You're right that the All Star Game is broken. I think you left out a few players from your example, but no matter since you got your point across (and it seems like this happens every year). I'll give a few ideas, both big and small, on how to fix this (some seem contradictory to each other):
The fans today choose the starters, and in a way, influence the reserves (but position players only). The fans vote like it's a popularity contest rather than voting for the most deserving player at each position. They vote very early, and often. First, I'd let fans vote for pitchers. I don't know how many pitchers are taken for the game, say 11 or 12, and vote for 9 starters and 4 relievers. Second, start the voting later in the season. With online voting widely available in many forms, voting doesn't need to start in late April just a few weeks into the season like it did 20 years ago when fans had to go to the games to vote. The internet changed that whole model. April is too early to figure out if a player is great. Start voting on Memorial Day. Third, get rid of the rule where every team should be included. It dilutes the product on the field.
Fourth and biggest, I'd take it out of the fans' hands and give the vote to the sports writers and baseball broadcasters. It kills the marketing of the ASG, so I see it as somewhat controversial, but give it to the people most capable of determining who deserves to be an All Star. In the end, it will make for a better game, one worthy of letting the winner determine who's league has home field in the World Series (and if you don't go with change #4, then remove the implications of winning). Maybe we can let the fans have a say to influence tiebreakers (but see also changes #1 and 3). I'll go a step further and say that the new class of voters also selects the manager and maybe even coaches (still mostly being other managers).
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