In my opinion there’s a potentially big market for a modern flat panel display that comes in a 4:3 aspect ratio. A display which is specifically intended to be used with retro gaming consoles or arcade cabinets.
There used to be 4:3 flatscreen displays but those primarily served as computer monitors and only got as large as 20 inches, and they came with VGA or DVI inputs. As far as I know, flatscreen TVs for the living room always came in a 16:9 aspect ratio.
It wouldn’t be enough to just make a 4:3 display, this gaming TV would need a built-in upscaler (like the Framemeister) to enhance all incoming signals to fit the HD display.
I also recommend that the display breaks with the standard 1080i resolution, and instead offers a unique 960i display that would be tailor-made to host the majority of systems. Here are all the (pre-HD) systems and their native resolution, along with the multiplier needed to fit a 960 display:
Unfortunately the SNES, NEO GEO, Genesis, and Phillips CD-i don’t fit the mold, so there would either be some stretching or a black border to preserve pixels. Overall a 960 display is a much better fit than 1080 for all systems.
This TV would need all the connectors of yesteryear: RCA, Component, S-Video, and possibly coaxial for systems that used RF switches. Maybe SCART as well, for folks in Europe.
EDIT: because this TV is exclusively for retro gaming, the remote won’t feature channels, playback buttons (pause, fast forward, etc), or number buttons. Just power, volume, and a bunch of input buttons. Maybe a scanlines toggle as well. Sure you could watch broadcast TV or Blu-Rays, really anything in a 16:9 ratio on this TV, but it would be letterboxed.
Dave's Geeky Ideas 
Dell P1917s is an option
For a retro video game enthusiast such as myself, as well as my brother who has a HUGE collection of VHS tapes, a television set like this would be a godsend. I want to upgrade the television set in my basement to a much larger model, but I can’t find any 4:3 flatscreen displays with all of the necessary connectors that I need. All of the television sets that DO have the necessary connectors are both hard to find and absolutely MASSIVE. (Just imagine trying to carry a 65-inch Projection TV down a flight of stairs.) A 65-inch version of this model you have designed would not only be the perfect replacement for my small CRT TV, it would also be very easy to transport.
If you were to start a Kickstarter campaign to have these sort of television sets manufactured and distributed, I would gladly be one of the first backers. Among the various ideas you have thought of over the years, I personally feel that this is the one which truly embodies a need that I have, but also that of many teenagers and adults who prefer older technology over newer solutions. People who have Autism in particular have a hard time adjusting to change. With a television set like this, they could continue to enjoy their favorite video games and movies in the face of technological advancements that leave fans of older formats in the dust.
Keep up the good work. I hope to see many more great ideas of yours in the future.
Kickstarting something like this would be too big for most companies, let alone me. Would be nice if a company that made displays, like Benq or MSI, weighed interest and did a crowdfunding campaign (much like Hasbro with their recent Jabba’s barge toy).
The above comment seems worthwhile, but is a bit on the small side.
I too have been on an exhaustive search for something like this. I actually thought I had found an answer recently, but alas it did not pan out. I had found a Pioneer PDP-V402 locally for $25. I replied to the listing, but the seller claimed to have broken the unit. Perhaps they did, perhaps they had a change of heart. I will never know for sure, but this indeed is exactly what the gaming industry needs to have back. This Commercial Pioneer display was designed as a 480p display, but had an optional downscaler you could order. It did all sorts of stuff and had a wide variety of inputs.
I do not know if you would want to mix digital and analog signaling on the same set and wind up with a hybrid model of sorts like we had in the mid 00s on most HD CRTs. There is simply too much lag introduced that way unless we find a good way to separate the signals. I’d opt for an all digital version and an all analog version of displays like this. Also steer away from OLED unless there is a good way to deal with potential burn-in. A full array, local dimming high-end LED with amazing brightness might rival that plasma look and come close on black levels. The 40” size would be perfect too just like Pioneer’s offering of old. I have never seen one of those PDP-V402 units before either. Good luck if you can get a hold of one.