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A study like this requires first that you define the term (numerically, objectively, what is a platoon). And then, that you gather the population of recent members that fit your definition and compare to alternatives and to expectations...not just to alternatives.
Step one: what counts as platooning?
I define a platoon as any one defensive position on a team where the leading recipient of playing time there got no more than 75% of the plate appearances, and where the percentage of plate appearances taken by opposing batting hand (r v l, or l v r) is statistically significantly higher than the league average.
I would find all team/posirions in the play by play era that fit the above description. I would find the platoon wOBA for each member of the would-be platoon in the previous three seasons or the entire previous mlb career if they haven't played three seasons. I would use those wOBAs and the distribution of plate appearances actually received by all involved players in the real platoon season to compute a projected platoon wOBA.
Thus, I would have a comparison between what the platoon actually accomplished and what we might expect given the playing time distribution versus each pitching hand. Then I would make the same comparison for positions that are not platooning examples.
If you compare the two platoon side to its projection...and then the non-platoon side to each projection and run an ANOVA-atyle treat to see whether the platoon gives Amy statistically significant advantage our disadvantage...you might get somewhere