With these two patterns now in mind, I pick up on details that just got filtered out before, lacking a larger framework to be plugged into. The other night, something caught my ear in Ridley Scott's commentary for Blade Runner. He explains why he loves shooting movies in anamorphic, using this scene as an example:
He says that the chess pieces are in sharp focus, Tyrell is just sharp enough, but then there's a quick fall-off in sharpness once you get past his body. It's not only very far-away objects that appear out-of-focus, like the two chairs in the middle of the right side of the frame. Even fairly close things are blurry, like the tables and chairs that are just behind him and to our left, not even as far back as the bed.
So, this scene shows the shallow focus, or the more restricted depth of field, that results from using anamorphic rather than spherical lenses in the camera.  The range of distance within which the image appears clear is a lot narrower. If it had been shot with a spherical lens, the greater depth of field would have allowed us to see fairly clear images farther back into the environment.
Hence, all other things being equal, shooting with an anamorphic lens produces an effect more like low-relief sculpture than like high-relief sculpture. (Relief means how far out does the sculpture project from its backing surface.)
The figure we're meant to focus on appears to be lifted out from an almost formless blur of a background -- and not a background that has its own depth, but like the flat surface of a building's exterior. And because things that lie much closer to us than the plane of the figure also show the same quick fall-off in focus, the plane of action does not appear to be high-relief. The depth of field is narrow enough that it looks like a thin slice of clear forms resting on top of a slab of blurriness, just like low-relief sculpture.
It also resembles paintings where the depth is restricted, although in painting it's usually due to placement of the figures within a narrow plane of action and hindering other depth cues. Compare Raphael's The School of Athens with David's The Death of Socrates. David's painting packs more of a punch because all of the action is concentrated within a narrow fixed distance from the viewer, like the action performed on a stage. When we look at Raphael's painting, our attention is diffused over a much greater range of depth, so that no single plane of action dominates our attention. Raphael wants us to calmly explore, while David wants to theatrically slam us in the face.
Obviously all sorts of other factors influence whether a movie scene looks more like a frieze or a diorama, such as the placement of figures within the environment. Still, the very choice of which type of lens to shoot with -- anamorphic or spherical -- affects this part of the movie's look as well. Anamorphic movies will tend to have a theatricality in their visual presentation, stemming from their shallower focus.
Finally, this allows us to rule out one explanation for why some directors and viewers like anamorphic -- i.e., that it provides a very widescreen aspect ratio. There have long been film formats that yield similar aspect ratios but that are shot with spherical lenses, from VistaVision in 1954 through the Super 35 of today. The reason that a good deal of those movies don't actually deliver on the promise of spectacular visuals is that they mistakenly thought the appeal of anamorphic was its wider aspect ratio, rather than its effect on depth of field.
Tomorrow or the next day, I'll put up a post with quantitative data on how prevalent anamorphically filmed movies have been since the lens type was introduced in 1953, looking at the top ten movies at the box office for each year. Then we can check if its popularity tracks the violence rate, to see how well it fits the broader pattern of rising-crime visuals having more limited depth perspective. I'll do some qualitative comparisons over time too. Finally, I'll try to include more pictures, to provide something more lively after this mostly analytical post.
 This result is indirect, but it still obtains. Here's the clearest explanation I found (from a comment left here).
The other thing is that anamorphic lenses don't have less depth of field per se, but because they have twice the horizontal view and therefore act somewhat like wider-angle lenses, usually one compensates by using a longer focal length -- for example, the equivalent to a 20mm spherical lens in Super-35 cropped vertically to 2.40 would be a 40mm anamorphic (more or less, ignoring the fact that Super-35 has a 24mm wide gate and anamorphic uses a 22mm wide gate). And a 40mm lens has less depth of field than a 20mm lens, the depth of field loss isn't due to the anamorphic elements, it's just due to the fact that you are choosing longer focal lengths to achieve the same view.