Projectors are way easier on the eyes than monitors though.

You're shining a bright light on a wall, which you are looking at.

With a monitor you are shining a bright light at your face, while staring directly at the lightbulb!

Doesn't bouncing off the wall just effectively make the "backlight" dimmer? The light reflected off the wall is hitting your face versus the light from the screen hitting your face. It's still light regardless.

If you're using a monitor in the dark the way you use a projector, you should turn the backlight down. If you're using it in a well lit room, the brighter backlight should have less of an effect.