Allow me to help shed some light on a perspective that seems to be lost on you.
When you are on a phone, you are having a private conversation, only connected to one person. When you go onto the internet, you are not just connecting to one place, and it is very much like leaving the privacy of your home to venture out into public, matter of fact, that is exactly what you are doing. You can not leave your house and be in public without someone seeing what you are doing. If you live in a small town then you know this to be even more so.
You can not achieve true privacy on the internet without crippling your operating system, and i'm seriously waiting to hear what the point in that would be.
@Umbra is very correct when he stated you would be better off watching what you divulge vs using applications to ruin your experience and possibly your OS trying to achieve what you never will.