I'm not categorically against the Moon being elevated to planet status, but the mechanism doesn't make much sense. Why should the exact orbital radius of the smaller body determine whether it's a moon or a planet? That doesn't comport with common understanding or historical usage of what "moon" means, and I don't see any important technical reason to introduce that as a distinguishing feature.
If two very similar bodies are orbiting each other, and each individually would qualify as a planet, then it makes sense to call both of them planets together. And in such a scenario, the barycenter will almost certainly lie between them, outside both of their surfaces. But that's not a good way of distinguishing binary planets from planet/moon systems, because the barycenter being outside of both doesn't guarantee any similarity in their masses. It makes more sense to simply determine a cutoff mass ratio (for example, maybe 4-to-1, but it could be anything). Below this ratio, both bodies can be planets, above it and the larger one is a planet while the smaller one is its moon. This comports better with historical usage and common understanding, and the quantity under consideration is more stable over time.