But many of the things I roll for behind the screen are for things the characters would not know about until or unless they experience it directly. As a player that would break my immersion, not enhance it.
So I'm not really seeing the advantage here.
Think of the initiative roll. The player does not know who goes first but he knows that as some point he has to roll and find out by this roll. It makes sense. Same about the unknown risks. To make it more clear: similarly as with the phases of combat in D&D (initiative phase, player turn phase, monster turn phase) in GW Warhammer combat is divided in a set of phases (movement phase, melee phase, shooting phase, magic phase). It is very easy to introduce a phase for unknown but expectable events such as battlefield events or risks. Furthermore, if you want to surprise your players you could introduce a surprise mechanic whose difficulty you could scale from easy to difficult according to what you want to happen in the adventure.