That's a valid reading of the text of the PHB, yes.
Going off of the above, I think this is where the discussion leaves the realm fo "what is" and moves into "what should be".
A lot of posts in the thread talk about worldbuilding, and the DM's vision of such, as the reason for including or excluding certain races as playable.
While at the end of the day that is entirely your prerogative, I can't help but question if some of the assumptions underlying the worlds you create aren't built on shaky ground, or are simply continuing tradition for tradition's sake.
There is a Twitter thread on the matter I found illuminating; a lot of quirks and idiosyncracies in D&D that players might just take for granted and DM's might perpetuate in their world and encounter design comes out of early editions' assumptions that the party held colonial ambitions; that one day they'd manifest some destiny and carve out a nice little fiefdom for themselves. This assumption has unconsciously been carried forward through the editions despite there no longer being any rules to support it (no rules for strongholds).
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Read the thread, and reflect on if the observed and highlighted assumptions have influenced the way you design your worlds, consciously or not.
I'll grant that the linked thread is not directly related to the current discussion, but I'd argue that its observations about the mode of play tie into why D&D holds (and perpetuates) so many assumptions about race that an outsider might see as weird or antiquated. I wonder if this feeds into the distaste for playable races outside the Original 4. Just something to think about.