Privacy as a virtue, not just a right

We usually talk about privacy as a right: something others shouldn't violate. But in my work I see people giving away their data voluntarily all the time, for convenience or a discount. The right isn't violated; it's waived, again and again.

I've started thinking of privacy as also a virtue: a disposition to protect the boundaries of one's own life and others', a kind of discretion or modesty. In Islamic ethics there's a strong idea of covering others' faults (sitr) rather than exposing them. Aristotle doesn't have a virtue of privacy as such, but he does praise a certain reserve.

Does it make sense to treat privacy as a trait of character we cultivate, not only a legal protection we demand?