Personally, I do feel that Humans should be the only race with 'diversity as a thing'.
Not in every way.
The aspects in which I don't want all demihuman races to be "equally diverse" are the (1) culture/history and the (2) mechanics. Where I DO want the same diversity is (3) alignment and (4) ethnicity links to real life.
(1) and (2) is why I like the PHB races: elves have a certain history which (mildly) influence your roleplay, without restricting it: you don't have to like magic because you're a High Elf, but you then have to deal with the fact that High Elves as a community do so. Every race with a delineated culture/history always provides you with the choice to roleplay anything between typecasted or against the type. Some demihumans even have multiple subraces so as to offer more starting points.
Humans as a whole do not have a typecast, which also means there is no such thing as playing against type. But the idea is often that a specific fantasy setting will bring back the typecasts by introducing different human regions and cultures, if you want.
As for (2) I am totally fine with demihumans having different stats than human. In general I do not like the idea that demihumans can mate with humans, I prefer them to be simply separate species, and the mechanical differences emphasize that. If the mechanical differences bother a player, I have no problem letting them use alternative stats for THAT specific PC, but I'll keep using the original for the rest of their kin.
On the other hand I do think that (3) alignment should be largely free for PHB demihumans, even though I like them as separate species, they are still the closest to humankind, so I think that morally-wise they should be more or less the same. However Drow and Tiefling are already farther away (in fact, I wouldn't have even put them in the PHB but maybe in the DMG) and therefore it's appropriate to me that they have an alignment "trend", just the same way I am ok with treating the alignment of races even farther away as a stronger trend, and then enforcing an absolute alignment on creatures that are totally alien such as fiends or mind flayers.
(4) When talking about skin colors or other traits that can be linked to real-world nationalities, I am very much against differentiating the close demihumans. This is because of fairness to the players, not to the characters. I have friends of all colors, as well as all genders and orientations, and I want all of them to feel represented equally by game characters. So yes to caribbean elves and chinese dwarves and arabian hobbits in my games.
Otherwise color and gender should have zero effects to the gameplay. I know that D&D is full of convenient color-coding of creatures, but that doesn't have to apply to ALL creatures. There is no reason why different colors MUST be applied to humans of different regions in order to be able to identify them by sight, use something else.
Drow instead are still pitch-black in my games, a coloration totally non-existent in the other basic races, so that it cannot be confused. A black elf (meant by the player to look like an african-american version of elves) will always be clearly different from a drow. And obviously dragonborn have their own funky colors, which has never been a problem since nobody expects to be able to apply real-world human traits to a reptilian.
It's fairly easy to see: if a demihuman race is still close enough to humans that real-world human colors and traits are applicable, then allow ALL of them, so that every player has representation. If it's far enough then you don't have to worry: orcs have grey-green-purplish skin, tabaxi have feline fur, so no players can feel underrepresented when playing one.