Well, the 2014 PHB kinda does that as it lists Realms ethnicities for human names... But I think the 2024 PHB will move away from that. Someone made a comment about this phenomenon a few days ago: games like Pathfinder can have an assumed setting in their core rules, but D&D can't because it is too popular. The closest thing we had was 4E's Nentir Vale, and I think that was heavily disliked for requiring all other settings in that edition to be retrofitted to Nentir Vale's aesthetic choices (Eberron getting a Feywild and Shadowfell, Realms having a pointless apocalypse to justify all red tieflings and AEDU casting etc.).I haven't read the entire thread, so forgive me if I cover ground already trod . . .
When the heroes struggle to communicate with the other characters they meet, friend, foe, or unknown, it creates tension and story opportunity. When they discover strange writing none of them can read, again, tension and opportunity.
Removing languages from D&D would be a mistake. But the way they are handled currently isn't that great, and I really don't like the way they are handled in the new Character Origins playtest document.
IMO, even in standard PHB D&D, there needs to be more world-building and the use of a "culture" category, which languages would be tied to. You could choose the elf race, then choose the high elf, wood elf, or dark elf culture, each with it's own language. Ideally, I would also try to create some culturally specific backgrounds for each race to hit those classic archetypes . . . but of course, players could customize and mix ancestries (race), cultures, languages, and backgrounds.
No more monolithic racial languages such as "elf". Three major elven cultures are described in the PHB, why shouldn't each have their own cultural traditions and languages? Same with dwarves, orcs, and everybody!
Of course, the problem then shifts to humans. There is no "human" language (unless you count common). And traditionally, humans are described as culturally diverse, but rarely are examples given in the PHB . . . its saved for setting books. I would like to see some human cultures detailed somewhat in the PHB, each with their own language.
Maybe WotC just needs to finally break down and marry the core D&D books with the Forgotten Realms setting, and use the cultural groups of the Realms in the PHB.
As for the need for langage for game moments, I'm not against the idea. But I don't think we need mechanical rules that say every player needs to know X languages from the Standard Languages list to achieve that. We'd be better off with leaving languages to fluff, to be determined by the setting's worldbuilding and what the table thinks is appropriate for each character to know. I think that'd be better for the simulationist goal of language use. And Common/Allspeak/Regional Lingua Franca would be the only mechanical standard language whose point is convenience.