Why can positive statements end with a negative question and vice versa?

I had a hard time phrasing the actual question title—hopefully this doesn't mean it's too subjective—, but I'm curious about why positive (or negative) statements can be terminated by negative (or positive) questions:

• You do like apples, don't you?
• We can't all be rich, can we?

Why is it (arguably) common to turn a general statement into a question like this when the intent remains the same? Is this a common use of a rhetorical question? If so, what is afforded by not simply making a statement without turning it into a question?

It is offering your conversational partner(s) a chance to contradict your current opinion. A (somewhat) polite version of "Prove me wrong" / "Am I right?"

Sometimes its a simple way to formulate a yes/no question: Yes, or no? I see it as related to the practice in Romance languages of adding ¿no? to the end of a statement to make a question.

If the answer is already assumed, though, its more of a rhetorical device known as aporia. Its a technique often used in examination of witnesses by lawyers in court. ie. "You were there when the crime was committed, weren't you?"