I run without a screen maybe 90% of the time.
One game I'm co-DM, and I have a habit of getting up and walking around a lot during the game. Either to divert attention to a different part of the room (to break up monotony) or to talk to a player who's doing something on their own. I put DM maps in folders, or on my clipboard with a couple pieces of paper over them to conceal them. I don't hide my notes, I doubt my players can read my chicken scratch, let alone read it upside down.
The rules information could be nice, but I have so much of it memorized, I don't feel it necessary. A few times when I've run newer games that I'm less familiar with screens have been handy as a reference, but often they're folded and to the side, not standing up.
I also play a lot of other games that don't require a screen, as everything that's concealed is in my brain.