Indirect, reflected light is easier on the eyes than a direct one like from TV's and monitor backlight.

Says who? A photon is a photon.

Also, having to be in a dim room focusing on a brighter light is itself uncomfortable.

Indirect reflected light like you get from a piece of paper, or an e-reader, or almost any everyday object, yes, I can see how that is easier on the eyes.

But in the case of a projector, the screen is lit by extra light; I'm not sure the situation is all that different from a regular monitor.