I think that the best screen serves two purposes-
1. The DM's side. This is obvious. The original 1e DMs screen had everything you could need. It was invaluable for a game so reliant on tables and matrices.
2. The player's side. You can't overlook this. For the most part, players aren't looking at your screen for information. But it does set a mood. And nothing has ever set the D&D mood like the original screen. Sure, there was the iconic Otus piece (spear, critter) that people still remember. But if you show either of the two panels to anyone who played at that time, it triggers something deep and primal, from the hours, days, and weeks of seeing that image and thinking about it, and having it deeply associated with D&D.
The Trampier two-panel piece may not be the best image in D&D, but it is certainly one of the most iconic images. And that's not wasted space.