usually the point of a peephole is to allow you to see who's at your door without letting that person know anything about you (including whether you're even there). it's a tool made with privacy in mind. that privacy kind of goes out the window when you've got a big fat window right beside it.
more to the point, however, a peephole really has no purpose on the door to a stairwell. privacy tools can be very useful, but not when they're put in places that don't make sense.