When you say car color, you use "car" as an adjective, it sometimes works to mean a possession phrase but not always.
Possession is often used for two instances of objects where one belongs to another, there is a car and it has a door, then you say "the car's door"
But in adjectives, you speak about one thing, for example if I say the "closed door", I am speaking about a door that is closed. Then if I say "a car door", I am speaking about a "door" which somehow is related to a car or cars, "car" is an adjective (a type or class), though its not a good adjective like it is "closed door"
As another example, for a book you may say "the book's chapters", "the chapters of the book" or maybe "the book chapters". In the latter case, which is not precise, "book" is adjective for "chapters" but the phrase could means "the chapters that belong or exist in a book". However, you can't say this for "car color". For example maybe "the color that is used for cars"?! If so, as the other answer pointed it may have some usages like:
I don't like chartreuse as a car color.
But it's not exactly an equivalent for "the car's color"