Ok folks, thanks for the detailed replies but I must have explained things poorly because you misunderstood my problem and feature request. Few things bug me more than displaying things with with incorrect aspect ratio so I am no “Aspect Ratio Murderer”. I’m the first guy to angrily go looking for the remote when I see a 4:3 image stretched horizontally to fill a 16:9 TV. I would never ever ever propose altering the display aspect ratio.
I’ll try to explain again. This time with pictures!
First off, all DVDs of TV shows and movies are anamorphic. DVD frames are always 720x480 pixels – an aspect ratio of 3:2. 3:2 is an aspect ratio commonly used in photography (think 4x6 prints) but is not the right aspect ratio for SD TVs or widescreen TVs. Here’s the 3:2 aspect ratio shown on the LCD screen of a Canon 5D Mark III (5760x3840 pixels; a 3:2 aspect ratio):

I suspect that 3:2 was chosen as a compromise between the aspect ratio fading from popularity (4:3) and the aspect ratio of the future (16:9). By being in between these two, a little stretching or squashing could fill either screen size. Stretching or squashing in this case means that the pixels are treated as rectangles rather than squares – which is what I meant by anamorphic: non-square pixels.
For widescreen (16:9), the pixels have an aspect ratio of 32:27 (1.185:1, width to height; note that pixel dimensions don’t have any physical meaning but are just included to show the exact pixel aspect ratio):

For fullscreen (4:3), the pixels have an aspect ratio of 8:9 (0.889:1):

For content that is widescreen (assumed to be 16:9 for now), there are two ways to get it to display correctly:
1. “Anamorphic widescreen” – A 16:9 image is squashed horizontally into a 3:2 aspect ratio (720x480 pixels) and a flag is set so that the player knows to stretch the pixels horizontally when playing back the DVD (the pixels are stretched by a factor of 1.185x as indicated above). The display size is 853x480 even though the frame is only 720x480.
2. Letterboxed – In this case, the fullscreen flag is set so the displayed frame is 640x480 (the horizontal size is reduced by a factor of 0.889 as indicated above). However, the content is widescreen so it will fill the available width (640 pixels) and its height will be 9/16 of this, or 360 pixels. So in this case, the display size of the content is 640x360 which would be stored on the disc as 720x360. Since all frames are 720x480, this requires the frame to be hard matted – 60 rows of black are added to the top and bottom to get up to the standard 720x480 size.
The problem I tried to communicate in my original post has to do with these letterboxed widescreen DVDs (#2).
On a 4:3 TV, this version displays fine:

But on a 16:9 TV, black bars are inserted on the right and left (source frame outlined in red below for illustrative purposes). The 16:9 TV doesn’t know that there are useless black bars at the top and bottom; it’s just displaying the image with the correct pixel aspect ratio and zooming as much as possible without cropping anything. Note that this thick black border is also present for similar reasons when viewing SD channels on widescreen TVs.
My feature request is for a zoom feature that would expand the video until its width matched the screen width allowing the top and bottom to be cropped off: i.e., “horizontally constrained zooming”. Because the source is letterboxed, only black rows of pixels on the top and bottom are lost:
For fullscreen content, this would mean cropping off non-black portions of the frame.
The workaround I have for now is to transcode only the content portion of the original frame in Handbrake, cropping off the black bars on the top and bottom but preserving the pixel aspect ratio information. Then the video is displayed with the correct aspect ratio and the TV can enlarge the frame much more before hitting the screen boundaries (typically until the width of the video matches the screen width). But I would rather set a flag in Plex and have Plex take care of it for me!
Another zoom feature that some might want is a zoom feature that matches the height of the content portion of the video to the screen height (vertically constrained zooming). I think this is what @trumpy81 was referring to:
This still maintains the correct aspect ratio but fills the whole screen with image at the expense of cropping off the left and right portions. This one is harder to do since for DVD and Blu-ray rips it won’t be obvious how much to zoom; you’d basically need a way to specify how tall the content portion of the frame is or the software would have to be very clever and figure this out for you (Handbrake does this but doesn’t always do it correctly).
iOS devices can do both of these kinds of zooming (horizontally and vertically constrained).
Finally, I’m aware that many TVs generally have zoom features to help with these sorts of problems. But again, it would be super nice if this could be set once in Plex and never dealt with again. Finding the TV remote, figuring out how the zoom feature works, which buttons to press, etc. is a pain.