But that's really a tiny field of view. Perhaps the easiest way to see this is that it's the same geometry as having a monitor-sized window in a wall at the same distance, and looking outside. That would be really tiny window, and you wouldn't expect to see much of the outside without getting a lot closer.
As a result, most pictures are taken at a wider field of view than what would be natural for typical viewing distances, to show more of the scene. Which explains the distortions that make everything at a distance appear tiny.
You fundamentally can't "solve" this without dramatically increasing the FOV that you're viewing things with -- VR being the obvious idea.
You can throw away the straight lines and shoot with a fisheye lens (no straight lines, wide angle, fairly natural depth), you can crop in (depth fine, but now I'm missing stuff around the edges), and you can shoot with a wide rectilinear lens (wide angle, straight lines, "exaggerated" perspective).
As far as I know, the answer is simply that your eyes aren't rectilinear but your brain fudges it to make straight lines seem straight when the image on our retina actually curves.
The effect is most prominent when standing in a small room. It's impossible to take a single picture of it that conveys what you want: a wide rectilinear lens will exaggerate how big the room is (and look weird around the edges), a "normal" rectilinear lens will be so cropped in that you can't see most of the room, and a fisheye lens will make all straight lines curve, especially around the edges. None of them really represent the visual experience of being in the room. Just look at how weird real-estate listings can get when they try to show you a picture of a small bathroom.
When you enlarge the photo and display it at the field of view it was captured at, as you can do in VR, the whole problem disappears and the photo just looks like the real world. Use two cameras and it'll even be in 3D.
If you intentionally use a nonlinear perspective like the Turner painting in the article, you can get an image that looks great flat, and still produces a wide angle of view and "natural" dense of depth with low perceived distortion, and will look fine from across the room or up close. It probably does a better job of recreating what it is like to be there than a mechanical linear perspective photograph. The only problem is you can't get images like that out of a camera.
That's true, but not the problem. Think about this logically. The goal is to show the exact same color at the same angle. If you achieve that (possible with VR, also possible with a normal photo but for a tiny angle only), it doesn't matter how the eye or processing in the brain warps the image afterwards.
Second, they point out that viewers almost always view pictures from the “wrong” location. A cornerstone of linear perspective is the idea that the viewer must be at the focal center of the image to view it correctly. If you view a linear perspective image from the focal center, it should be like looking through a window—indeed, Leonardo da Vinci wrote that linear perspective images only work from the focal center. Yet, in reality we don’t do this. Most of the photos we look at would have to be viewed with one’s eye a few inches from the page. People in art galleries walk all around and view paintings from all sorts of angles. Hence, the whole idea of linear perspective falls apart.