I ironically agree that the race ability score improvent has defined what a race "means". The reductionist tradition has reduced each race to almost nothing except an ability score improvement.
D&D 1e defined a "race" by means of a selection of ability modifiers and a prohibition against certain classes that the race is forbidden to take. This mechanical usage is the "essence" of what a race means. Other traits like darkvision (infrared) existed but were less consequential. The 1e mechanics were primitive and still evolving, and gaming culture was expected to express other characteristics about a race by means of "roleplay", such as if elves are supposed to be magical and artistic the players simply pretended them to be despite nothing about their 1e mechanics articulated their magical or artistic prowess. Indeed, 1e elves were forbidden to be innately psionic and forbidden to be Druids and therefor forbidden to be Bards. They could not reach high levels of Wizard (magic user), only the nonmagical Rogue (thief) was an unrestricted and unlimited class. Despite the narrative description of the opposite, the elves mechanically hated magic, hated nature, hated art, hated music, hated innate magic, and by the way, even hated being a gish (fighter / magic user). I find the 1e mechanics incompetent at cohering mechanics with the flavorful description. Unfortunately, this "tradition" has continued to straightjacket the elf mechanically, despite the dissonance of the flavor being the exact opposite. D&D roleplay required doublethink, holding two contradictions to be as if true simultaneously.
Fortunately, D&D mechanics continue to evolve. The class prohibitions and level restrictions were widely rejected immediately, and even 1e began the infinitude of elf subraces to slip past the race-class dissonance, and swap the ability score improvements. Similarly, mechanics to handicap female characters were widely rejected immediately.
By 2e much of the problematic 1e mechanics were gone. So elves can be Druid and powerful Wizard, and no more handicapping women.
3e systemized the random ad-hoc mechanics of 1e and 2e, by making ability bonuses the fundamental mechanic of the gaming system. Unfortunately, the dissonanant race ability score improvements carried over.
Inadvertantly, 3e thus made the earlier bad design whose bonus and flavor contradicted each other, into a fundamental definition of a race, with far reaching gaming consequences.
4e continued the ability score improvements but began making them fluid by granting choices of equally weighted ability combinations for each race. Moreover 4e gave each race a powerful race feat (like Misty Step teleportation) that was often as good as the ability score improvements. Moreover, later options often swapped race features, to specify certain flavorful tropes while maintaining balance (such as swapping weapon proficiency for spell focus or spell casting options).
Originally, 5e removed the race feats and doubleddown on a weighted ability score improvement restriction, even when it brightly contradicted the multiple flavors within a race. 5e used a heavy hammer to force a rounded race concept thru a square hole. Fortunately, the unwise start has softened, by 5e now making the ability scores float, to fluidly explore the many tropes and concepts that exist within each race.
In sum, the D&D tradition has made a "race" mean almost nothing except an ability score improvement. The other features are less significant, and peripheral as subraces or options. Besides their reallife historical origins from racist assumptions, the ability score improvements are less good gaming design, that prove too inflexible, and less able to quantify the various narrative descriptions with the race itself.
I hope D&D 5e returns to the tradition of powerful race feats and swappable options, for each race to be a more diverse and complex community.
