Fairness.
Fundamentally, D&D is a social game that you play with other people. Different people have different methods of handling the game, of competition, and of certain innate ideas of fairness- this is why, for example, the concept of "sharing the spotlight" has become more important in RPGs. However, this is an aspect of the social compact that often gets overlooked when it comes to PC ability score generation.
Well fairness... and asymmetrical ability score to class design.
If you want to play a melee warrior, you had to roll high STR. There was no DEX duelist at the beginning. And even now in 5e, only STR, DEX, and CHA allow for melee builds.
Same with casters. Originally there were only 2 spellcasting classes with 2 casting stats.
Only in 4e did you have warrior, casters, melee, and range be in almost every ability score.
This is before you get to later editions with
Multiple
Ability score
Dependence. When some classes require 3 good rolls whereas others only needed 1.