Since we want to maintain normal frobbing of doors and handles, how about this proposal:
1 - Create a new entity you can bind to a door, in the spot where you'd normally put the handle plate. This entity uses a model that looks different than the current handle plates. It includes an obvious spot where you'd place the handle, and an obvious over-large keyhole. This entity would look the same--and provide the same functionality--on either side of the door it's bound to.
2 - If you crouch in front of one of these things, and you're close enough to the door, you're presented with a screen-filling GUI (like the one Obs used in his proof of concept). You can then see and hear what's on the other side of the door.
3 - Moving away from the door or standing up returns you to a normal view.
Advantages of this:
1 - Retains normal door and door-handle frobbing.
2 - Provides a visually different clue that the plate's keyhole can be looked through.
3 - Doesn't require leaning.
4 - Doesn't affect existing maps where it obviously was never used.