But goliaths aren't going to be better barbarians due to Strength because, when it comes to weapon damage, Strength and Dexterity provide the exact same bonus. A goliath barbarian with an 18 Strength who is wielding a shortsword is going to be inflicting 1d6 + 4 damage from Str + whatever their rage bonus is. A gnome barbarian with an 18 Dexterity who is wielding a shortsword is going to be inflicting 1d6 + 4 damage from Dex + whatever their rage bonus is.
The difference here is that goliaths, because they are Medium, have no penalty when using Heavy weapons. Thus any Medium creature is automatically going to be a "better" barbarian than a Small creature because they can use Heavy weapons. No matter whether they get a +2 to Strength or not.
That, plus the fact that goliaths gain Powerful Build, means that goliaths are stronger than gnomes automatically. No need for an ASI to add to that.
(And, of course, that assumes that a "best" barbarian is the one who inflicts the most damage.)
(And the next question is, why is an 8-foot tall, sturdily-built goliath equally as strong as a 6-foot tall, slender githyanki but stronger than the equally tall but heavier loxodon, even though the loxodon also has powerful build, can lift much more than a higher-Strength githyanki could, and can heft a gnome using only its nose?)