Would making the PHB, MM, and DMG as setting neutral as possible fix that problem? Or, to your mind, should the game actively promote more inclusive settings?
Not everything has a "neutral". But in general, yes, I believe the core rules should be fairly neutral or generic. For me, that's less about inclusivity and more about the D&D core being the basis that all the other settings are based off of. WotC should promote the settings that sell best.