"Screen Generation" Sorry, I'm using terms that apply to the CE industry. We even have "engines" in LCD and DLP TVs. If you will do a Google search using the terms screen generation and rendering you will find many references to "generator" as in computer generation of video. You may be more familiar with "render". As Ray tracing and OpenGL becomes more popular to reduce the cost of producing content rather than rasterization, my understanding of how the terms are used in my industry would have generation of the screen rather than render as more accurate. I have read and understand that the OpenGL process descriptions do use the term render.
The same could have been said for 1080P. Low demand and expensive for the first 3 years. The rate of acceptance for 4K is debatable because we have just recently reached a point where 1080P is in just about every TV over 32 inches.
Have you done any research into 4K TVs? Most of the 4K LCD TVs offer polarized 1080P 3-D with 4K, rather than shutter glasses. The idea is to make 3-D more attractive. 4K is easily and cheaply possible on the player end as everything is already in place. IF you have the hardware for 3-D, you just about have the hardware for 4K. The HDMI 1.4 specs reflect this.
The display end is another matter. And there can't be any cheating like they did early on with 720P TVs accepting 1080P and displaying at 720P. For the 1080P 3-D to use polarized glasses, it's necessary to have the full 4K display.
For projectors and rear projection DLP, it's possible to have a much less expensive 4K TV, just slightly more expensive than a 1080P.
And yes, "So there's absolutely no incentive on anyone's side to pursue another large jump in resolution." that is probably true for developers as well as Sony and MS and is possibly why the next generation Game machines have been shelved, it's mentioned in the article cited by Shifty that started this thread.
4K TVs will be released and will become a standard within the 10 year life of a PS4 just as 1080P did with the PS3. Consumers will expect support for their new TV during that 10 years and any Next generation console would have to support it eventually.