In English, proper nouns are always capitalized. Since there is only one sky I would expect it to be a proper noun and capitalized. But it seems it is treated as a common noun and not capitalized. Why is this the case?
Proper nouns are capitalised, but "sky" is not a proper noun.
Proper nouns name specific people, places, objects or concepts. And so for every proper noun, there should be a generic noun (or nouns) that name the type of that noun:
John is a man.
Paris is a city.
Wednesday is a day of the week.
But can you do that with sky?
Sky is a ....?
Moreover (as mentioned in a comment) "sky" isn't a single specifically named thing, as there is the "night sky" or "the daytime sky", or "a beautiful sky in Kansas" and so on.
Now, sometimes we use "majestic proper nouns". If a noun is a specially important it might be treated like a name. This is particularly common with nouns associated with God, or with common nouns used in place of names.
John is in Heaven now.
The Queen visited our factory.
The Universe formed 13.7 billion years ago.
But this would rarely be a justification to use "The Sky" as a proper noun.