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The ultimate arbiter for every defensive-looking stat (pitcher or fielder) is pretty basic. Was an out recorded -- and if not, how many bases were advanced?
Imagine we could definitely measure that Halladay does indeed produce lower than normal mph for ground balls -- and that said groundballs tended to go more toward the left side of the mound. And that compared to other pitchers, he was the best at this. Yes. That could be considered a skill. But, having that skill doesn't mean anything (baseball-wise), unless it produces more outs.
Perhaps there is a break-point where he's soooo good at this that he ends up surrendering a higher percentage of infield hits. What's the result? He gets the same number of outs as the next pitcher on groundballs.
This is why we NEED the Sabes -- to take a theory (like Halladay is better at getting GB outs than everyone else), and attempting to quantify it. Well, BABIP doesn't answer that question specifically. But, given his BABIP -- I think it does pretty clearly state that if he does have an edge there -- he's giving it back elsewhere.
Ultimately, offense, defense, pitching can all be viewed as bases-per-out. We can't easily segregate pitching/defense, but we can count the same things the same way for each pitcher and see where players thrive or flail compared to those norms.
The what happened can be (largely) quantified. The why it happened will always be subject to debate.