The difference is the the monster's AC, HP, attacks, saves are all mechanical. If you abstract away from the lore of the monster (alignment included), changing the AC, attack bonus, damage, etc actually do make the monster more or less difficult in combat. On the other hand, a Balor, a Wraith, and a Hill Giant are all chaotic evil, but this neither changes the math of the encounter, nor does it, I would argue, give the DM a very helpful baseline for how to roleplay the creature, in or out of combat. An Aboleth and a Kobold are both Lawful Evil, but you would never play those monsters in the same way (right??).
For combat, 2d6 reaction tables and morale scores are, IMO, more useful tools. Beyond that, I think a system of 'tags' would be more helpful than alignment (aggressive, cowardly, diplomatic, cautious, etc).