What's the difference between a screen emitting X light as a primary light source and a sheet of paper emitting the same exact amount of light, as a secondary light source ?

The amount of light coming to your retina stays the same..

Just lower the brightness until it matches the amount of light reflected by a sheet of paper placed next to the screen.

If you can't read the paper, turn the lights on. Being in a dark room dilates your pupils which makes them even more sensible to bright light...