I suspect that XOR is popular because of the property that XORing data cannot reduce its entropy: 128 truly random bits XOR zero* are still 128 truly random bit

I suspect that XOR is popular because of the property that XORing data cannot reduce its entropy: 128 truly random bits XOR zero* are still 128 truly random bits. The benefit you get if you XOR is that if there are mathematical correspondences in your data, you are likely to hide them by XORing with some key.