Winston, it's late, I just got home, and I skimmed your argument. It doesn't make any sense. The entire point of UZR is that errors aren't the only way you can hurt your team. There are lots and lots of balls that an average shortstop would field, but get by Jeter, so those are all costing his team, too.
And relating to Saro's comments about stats, and generally, the complaint that people have with "stat-heads": for baseball's entire history, people have been evaluating players based on stats. Have any of us seen Babe Ruth play? No, but based on his stats we know that he's good. For decades, writers have been judging players by their stats and children have been collecting baseball cards and memorizing stats on the back of them. Why is player X really great? Because he hit 30 HR, or had a .300 batting average, or got 100 RBI, or stole 50 bases, or had the best fielding % in the league.
What people don't like is that some people, instead of blindly buying into the stats that were promulgated by the media and MLB, have actually dedicated a tremendous amount of time and energy in an attempt to better understand this game that we all love, and have discovered and developed better stats that do a better job of evaluating players. We've always used stats to argue about who deserves to be MVP, who should be in the Hall of Fame, who was better - Mantle or Mays. Now, we have stats that answer these questions much more accurately. Can they do it definitively? No, but they come a lot closer.
The nice thing about the old stats is that they really didn't answer any questions.
"Player X is better than Player Y, he hit 20 more HR. "
"Oh yeah, Y had a much higher batting average. That's much more important."
There's no way to settle that argument, everyone can think they're right, but nothing is settled.
But, by using a stat like EQA, we can easily evaluate who is the better overall offensive player. Sure, there may be a situation where we'd rather have the homerun hitter up or a situation where we'd rather have the batting average guy up, but over the course of a season, we can evaluate who is better using one scale.
I think people fear things they don't understand. They like being able to argue whatever they want, and the more advanced stats don't let them do it. Stats can be used to argue anything, but the beauty of stats like EQA is that they provide a consistent way to evaluate players.

Oh, and as far as the Yankees, while they may not employ Billy Beane or Bill James, I think it's fairly clear that they have focused largely on the "Billy Beane model", by acquiring guys who get a lot of homers and walks, and pitchers with high K/BB ratios. I think the Yankees are one of the clear examples of the model working.