Using "of" in simple examples "the car of my sister" tends to sound like translationese. In most examples when the noun is simple, you can use the possessive.
However, a noun can be complex. "The tall man I met at work" is a noun phrase, and *"The tall man I met at work's teeshirt" is problematic. It becomes hard to parse such phrases. Using "of": "The teeshirt of the tall man I met at work" is less likely be confusing. There are other ways to express this.
Using "of" allows me to put an article or another determiner with the object being possessed: "He is a friend of Sue" to imply that Sue has many friends. Consider now the word "part". You can say "a part of the sentence", but not "a sentence's part". Again, by using "of" you can place the article with "part".
Sentences with "of" can be more flexible because you can more easily add modifiers, sometimes that is convenient.
Then there are proper nouns with of as part of the name. You say "Bank of Scotland" or "Houses of Westminster", because it is part of the name of these institutions.
No doubt there are other situations in which "of" is preferred.