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I put the Cubs/Angels in the calculator column mainly because both teams are steady teams that lack situational hitting.
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Quite simply, this has nothing to do with building a team via stats or not, and that's your misconception. I recommend doing a bit more research on the subject. Beyond the Boxscore is a great place to read.
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And, I'm not saying purely that batting average alone is the end all-be all stat, just that tossing it aside for OBP does come with some flaws.
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First off, you don't understand OBP if you think it's only walks. It is, simply, how often a player avoids getting out. As outs are the only limited resource in the game THIS IS ABSOLUTELY CRITICAL. There's a reason it correlates much better to winning and scoring than batting average: preserving your outs is not the only concent, but it's the most important. Batting average tells you really little of importance that OBP doesn't.
What OBP lacks is looking at the quality of a player's at-bats. Batting average doesn't do this, either. It treats a single and a home run as the same. Slugging Average does not, and thus suplimenting OBP with SLG gives you a fantastic way to evaluate a player's plate production that BA doesn't.
Essentially, the two most important things for a hitter are 1) avoid getting out and 2) advance yourself and other base runners as much as possible. Batting average doesn't tell you how often a player avoids getting out, and it doesn't tell you how much he advances himself and his teammates. OBP and SLG and OPS can be improved upon, but they are just as simple and available as batting average and tell you much more.
That is neither here nor there, though. The point is that I don't think you have much of an awareness of what teams who build with data analysis are trying to do, or which teams do that. I emplore you to actually research the subject if you want to be an authority on it.
And the Rays just turned around a franchise and went to the World Series with that approach. The A's won far more games year after year than they should have been able to on their dollar and have now built perhaps the strongest farm system in baseball with that approach with that approach. The Indians were a game from the World Series with that approach, and they lost to the Red Sox: a team that has won two World Series with that approach.
One thing I wonder if you understand is that all data doesn't tell you the same thing or look at the same things, and most teams who construct that way are looking at data that you probably haven't even heard of.