I will have to show this to my wife. The solution is clear. I need to get a 100" screen to sit 12' away.

I don't know about the math of it all. I am sure it's valid but there is always some thing an equation doesn't cover. History of science is replete with theories that claim too much domain of efficacy in the beginning. I am seeing better picture in some stuff. Not all but some. I think they are just upscaled stuff. I haven't seen a native UHD material yet.
What often happens in the real world is that in the
digital realm, a
higher resolution camera is used to film in order to get good quality at a
lower resolution product. So a concientious director will want to Film in 4K because he wants his film to have a better quality on Blu Ray than would otherwise be possible.
Transferring from real film, which can yield a much higher resolution than you would think, to digital involves still many factors besides the physical limits of making a transfer. It takes a lot of effort to do it right.
So right there, you can see there will be a lot of different quality options which have to be decided upon as resolutions get higher and higher. There is still plenty of room to get amazing digital images from 70MM films, but how many of those films are available? And how much money/effort will the average 4K product have in it?
Digital cameras should be 8K to produce 4K content. There is a lot of work to do this and not enough bodies to do it right, so there is not much content. Anything you see that is 8K and most of the good 4K stuff is in some special event, made to show off the technology.
So for Blu Ray and digital, the latest quality movies were shot with 4K and even 8K cameras.
Consumer 4K TVs are actually usually 3840 X 2160, the dimensions of my early generation "4k" monitor from Dell (got it onm sale for $300

) The marketing term is actually "4K UHD" in case folks actually do the math and want to sue.
When I have seen 4K content on my computer from the internet, the production people had often "blown out" the contrast because 4K can really show flaws in closeups, flaws that are unacceptable for movie watching. I think that there will be an amazing amount of post-processing and CGI work when 4K movies are common. You should watch the movie "The Congress" currently on Amazon Prime about the future of movies and the world itself, look for an appearance by Reeve Robs.
Even for this "fake" 4K technology there is not a lot of content out there. Streaming will lag behind a lot I believe, and will be "up to 4k". Streaming of 4K would be a miracle at the present time, as the special HEVC (High Efficiency Video Coding)/H.265 compression standard is required to do it at the present as I understand it. And for Youtube 4K you need another standard. Also you would need consistent high speed internet, which I can't seem to get. I can download at incredible speeds now, but not consistently. Hence the new Amazon Fire box has 8GB to buffer movies so 4K streaming can work in the future.
The good news for us all is that I can watch things produced for 4K on my HDTV (almost 2K!) right now and benefit, so the transition to 4K is good for viewers with HD. But if I had a 4K TV I think it would be tough to just watch something and have a good picture quality. The TV will need to go excellent upsampling as my Sony 40" 4x3 CRT did - it made analog cable look good in 720p or even 1080p. And shows that were produced for 1080p that were still broadcast on analog cable (such as Conan O'brien and the evening news) looked like a real 1080p!