Let's get subjective.Sharpness, detail and black levels and neither home would I ever want a projector or screen in our family room.
You are spot on. Virtually any quality TV will smoke most any projector in black levels and sharpness... most TVs will also out perform most projectors in brightness as well. That said, I like movies. Watching movies on a projected image looks more like going to the cinema and I like that. More than that, most video displays do not match looking out the window at nature... they are hyper real with greater detail and a sharper image than you get with the naked eye.
It is up to the viewer to decide which he prefers. I like projectors, but totally understand why you may prefer an emissive display.