I get this question quite a bit here and on YouTube, and recently answered in the question thread for a post here, so I thought I’d add the answer here as well. This is slightly amended from the original.
The reason is field of view. While the front window of the cabin is about 46″ in diagonal, from the seats in the cockpit the actual field of view is much wider, especially if you want both the left and right chair to have an immersive view without seeing the edges of a screen. The projection screen hangs just two inches in front of the front edge of the cabin. It’s a 100-inch screen, and even with a screen of that size if I lean forward too much over the glare shield I can see the edge of the screen. One option would be to tilt-mount a big display to the cabin’s front-slanted lumber, but that would probably not look immersive as the viewing angle would be at a significant down-facing degree. I would love to have a TV for the front view just to have similar view quality all way around, but 100-inch TVs are a bit out of the price range right now (NEC makes one for $33,000 – the price of a nice used Cessna 172l; Sharp makes a 90 inch for six grand). So I go with the projector. I use an ultra-short throw because with the height of my ceiling and the height of the cabin, a projector mounted too far back casts a shadow over the screen as the beam hits the top of the cabin. So the projector needs to be really close to the screen (in my case, just about 24 inches). Finally, I also like the projection screen because I can look around the edge of the window a bit to find the field on final approach, just like in the real world.