Please show me a non-elf race where different narratives necessitate floating ASIs.
To represent the D&D elf traditions of earlier, as well as the current descriptions in 5e, the floating ability score improvements are necessary.
For other races, the floating improvements seem useful, to focus on one of the specific tropes, while alleviating any conflictive mechanics.
The hobgoblin comes to mind because of its complex tradition, and because of its unfortunate stereotyping.
In D&D 1e, the hobgoblin is nonmagical, average intelligence, with a military vibe, relating to leadership, morale, tactics, battle formations, military engineering, competitiveness, gory brutality, and Evil. Its illustration in the MM (Monster Manual) wears Japanese-esque samurai-like armor, possibly suggesting a grotesque caricature of a Japanese WW2 enemy.
By 3e, the MM illustration wears Roman-esque armor, with a vibe of imperial brutality, but the earlier "samurai" meme will continue to resurface elsewhere. The hobgoblin becomes a player race featuring Dexterity and Constitution. They tend to be fighters and, now, rogues, but now spell casters exist, either clerics or low-level "adepts" that prefer damage spells.
By the 4e MM, the hobgoblin groups together with bugbear, under the goblin entry, as kinds of "goblin". (In 5e, the three will come to be called "goblinoid" to disambiguate from the goblin proper.) The hobgoblins "live for war and bloodshed", are "aggressive and organized", conquerors and slavers, and "reserve a special loathing against all fey". The hobgoblin statblocks are all nonmagical military personnel, "grunt", "warrior", "archer", "soldier", and "commander", except for a magical "warcaster" who seems like a kind of religious military chaplain yet is more like a Wizard, and for a "Hand of Bane" who seems a kind of paladin.
In 3e and 4e, the statblocks normally list the ability scores as primary Strength then secondary Dexterity/Constitution (usually equal), except depending on the concept Intelligence or Charisma gets a jump, and these abilities continue in the 5e MM too.
Despite the normal "brute" build, with primary Strength, the player character ASIs conflict. Player character stats abandon the ubiquitous Strength improvement. 3e improves Constitution and Dexterity. 4e improves Constitution and Charisma for military leadership. 5e Eberron Rising improves Constitution and Intelligence for military tactics.
In sum, for the D&D hobgoblin tradition, every ability score improvement can be +2, except perhaps for Wisdom. (Notably, even the religious leaders seem either Charisma or Intelligence.) So a floating ability score improvement to represent
Strength,
Dexterity,
Constitution,
Intelligence, and
Charisma, is necessary to represent the hobgoblin tradition.
After 3e tended to Romanize the hobgoblin, 5e unfortunately returns to its roots as the evil Japanese-esque meme, via the MM illustration of armor, and the Eberron Rising "Saving Face" trait.
Currently, 5e is in the process of making alignment an individual choice for humanoids, including the hobgoblin. Likewise, hobgoblin culture is becoming more realistic and more complex, comprising diverse individuals who may or may not conform to the "average". Volos explores what hobgoblin Monks can look like, appropriately, given the Dexterity tradition. Intelligence and Charisma suggest powerful spell casters can rise in prominence. I personally feel, a reallife culture must never be a model for a monster concept that is a grotesque version of a human, as the hobgoblin is. Hopefully, the diversification of alignment and abilities, helps make any unintentional recycling of unfortunate traditional memes less egregious.
I love the current 5e renaissance of the hobgoblin returning to its mythologically accurate roots as a fey being. A UA lists the goblinoids as having fey ancestry, and I expect we will see more in the upcoming Witchlight book, and perhaps Strixhaven too.
In reallife, the goblin and hobgoblin are British folkbelief. Where a hob (domestic gnome) is a helpful fairy, the goblin is a harmful fairy. In this context, helpful versus harmful has to do with how much they participate in human society. So the "hobbit" is a very humanlike house being. But a goblin tends to be dangerous to human communities. The term "hobgoblin" is an oxymoron, being both helpful and harmful simultaneously, and is a nickname for a practical joker, with a painful sense of humor. In the sense of the hobgoblin as a fey being of fate, the victims who suffer from the pranks often richly deserve it. Karma is at work. Shakespeare details Puck as a "hobgoblin" who is the royal jester of a fairy court, in Midsummer Nights Dream, and if I recall correctly adds other information about the reallife concept of a hobgoblin elsewhere in passing. Humor and being funny is the key concept of a hobgoblin.
For the D&D tradition, the goblinoids are now fey ancestry, like the elves. Also like the elves, there are still fey goblinoids who never left the Feywild. Fey is a new tradition opening up, but makes sense in the context of both the D&D tradition and the mythological accuracy. Earlier editions mostly lacked the concept of a Feywild (despite occasional references to the Faerie or Fairyland), so there are few early traditions about it. In 4e, the goblinoids are material ("natural"), but often populate the Feywild. In 5e, there are fey hobgoblins and material hobgoblins. Where the material ones have fey ancestry, it can help explain why at least some of them hate all fey. Perhaps they entered the material world to punish humans, but the other fey decided the hobgoblins went too far, and perhaps the fey went too far?
At least one material hobgoblin culture tends to obsess on military conquest, whence "evil". But the fey hobgoblin culture might tend to obsess on humor, whence "good", albeit in a painfully punishing funny way. The UA fey-ancestry hobgoblin traits "fey gift" and "fortune of many", involve the flavor of karma-like "reciprocity" that is appropriate to fey as they personify fate.
Interestingly, because these hobgoblins are fey, their Intelligence and Charisma comes to forefront as hobgoblins who are powerful spellcasters.
In sum, the Tashas rules that float the ability score improvements allow the hobgoblin to better represent the complex D&D tradition, helps mitigate unintentional reallife racist memes, and facilitates the exploration of the Feywild setting.