"Kaus kaki hitam."
Having somewhat conservative tastes, I tend to wear black foot-shirts as well.
Why not "(the) socks are black"? Why "Saya kuat" is "I am strong" yet similar gramatically phrase [(pro)noun + adj] cannot be treated as a sentence?
Noun and pronoun are not the same. Pronouns don't get adjectives - you don't generally say "strong I", and so "saya kuat" is not ambiguous. I don't know Indonesian, but in Hebrew "socks are black" has to have a copula, so assuming Indonesian is like Hebrew, this can only mean "black socks".
Indonesian does not require a copula, indeed it is debated whether it has one. The adjective in this case would not be modifying the pronoun, which is in the possessive position. I do not know why this couldn't be a sentence either, though an Indonesian might use ada or adalah for clarity, I guess.