There is no option to remove private browsing. Even if private browsing is not used it is still possible to clear the history using the clear recent history option.

I know the history can be cleared but not everyone knows there are other ways to check what type of sites have been visited. However, if private browsing is used I can't check anything. If the history is erased by a certain person I'm okay with that because I can check other things that they don't know how to erase yet.