Again, that is the system that has been in use for 50 years. ASI, it varied a bit over time as to which races and had how many but overall it had remained fairly constant and helped out establish both lore and the mechanics of many races.
Well, actually... Aside from the nitpick that D&D isn't yet 50 years old (it's 46), in OD&D there were no subraces of dwarves or halflings, and elves are said to have woodland and meadow varieties. That is, until the Greyhawk supplement, which gave hill, mountain, & burrower (gnome) dwarves, wood, high, meadow (faerie), & wood elves subraces.. However, none of these subraces were detailed and all had the same abilities. Also, none of the demihuman races had ASIs. The Holmes Basic set likewise had no ASIs. It differs from the Greyhawk supplement in that there were no dwarven subraces and elves had two subraces (high and wood) which were only mentioned in passing in the monster section. The Basic D&D line (from B/X to the "The Classic D&D Game") made the demihumans into classes, dropped the subraces entirely and had no ASIs.
1e AD&D reintroduces many of the subraces in Greyhawk and add a few more in the original Monster Manual—Hill and Mountain Dwarves, High, Aquatic, Drow (no details, and no modifies from the standard, high elf, entry), Grey (Faerie), & Wood Elves, and Hairfeet, Tallfellow, & Stout Halflings. In the Player's Handbook, Hill and Mountain Dwarves use the same entry, Elves are limited to High Elves, and of Halflings only the mixed and Stout have (slightly) different mechanics. This is the first version of the game to have ASIs. Other subraces are introduced in modules, the Fiend Folio, & Monster Manual II, and playable subraces are introduced in Unearthed Arcana.
In the 2e AD&D Player's Handbook, it makes no mention of dwarven or gnomish subraces, uses the same racial features for all elven subraces, and halfling retain the standard/mixed/Stout subraces and their differences. The ASIs for all remained the same as in 1e—except gnomes which now have +1 Int & -1 Wis (whereas they had no ASIs in 1e). The Monstrous Compendiums & Monstrous Manual further detail the subraces—here we first get that Mountain Dwarves are isolationists, Grey Elves go from living in meadowlands to living in forests, and gnomes start having shorter beards than dwarves. In later 2nd supplements, the other subraces (including new ones, like Forest Gnomes) are introduced as playable and often have different ASIs from book to book.
With 3e D&D, the Player's Handbook restricted demihumans (no longer called demihumans, though) to 1 playable subrace—Hill Dwarf, High Elf, Rock Gnomes, & Hairfeet (now renamed Lightfeet) Halflings. +1 ASIs became +2s but otherwise remain the same. Except Gnomes. Again. The Monster Manual opens up the other subraces (though their ASIs are rather hit and miss—usually miss—with regards to what had come before).
As for 4e, I will leave it to someone more knowledgeable on the subject than me as I never played it. I do know that there were changes (like high elves becoming eladrin), but beyond that I'm wholly ignorant.
In 5e, all ability score penalties were removed. Dwarves retained their bonus to Str, elves and halflings their bonus to Dex, gnomes went back to 2e's bonus to Int, and everything else is kind of wacky.
In conclusion, ASIs existing and their placement when they dead are not entirely consistent throughout the editions. So an appeal to tradition, which must stand on the merit of things other than the tradition itself, is less than solid ground as the tradition is actually fraught with inconsistencies.
/pedantry