Nice write up. I was recently looking and the reduced sizes of silicon chips in production.

The one thing someone else mentioned though, is that you make chip size is the only factor to consider. I'm sure they are other 28nm chipsets more powerful then the PS4? If so, 14nm should do fine in providing another 8x leap if sony are will to spend a bit more on components this time.

Its about timing. Yes, if they wanted to release consoles on a 14nm process in 2017 it would likely be possible. But why do that when you can make the jump to a 7-10nm process with all manner of other developing technologies in just 2-3 more years. 

Maybe because it's cheaper and the technology and yields are preferable over a brand new form factor? There is no guarantee that Intel will stay on top of their schedule for the shrink. The jump to 14nm took a lot longer than anticipated as well. 7/10nm are a whole other level than 14nm. If they have trouble with yields now, just wait for when the first samples of 7nm roll out.

I dont think they should plan for 10nm. First because it's risky and second because I need new consoles earlier than 2020.

No chip sizes aren't the "only" thing that matters. but it still stands as the most straight forward indication to performance gains in a chip architecture. Mind you, a reduced fabrication process doesn't even mean u just get or can get more transistors. It means you now have more room to work with in a given sized die. So you can add in other specialized components on the chip that improves performance. 

What kind of power leap to you thing we could see by 2017 on 14nm chips within $399 price bracket?

There's just one important factor that almost everyone is missing and that's the power limit ... (No I am not talking about performance or Tflops ...)

There isn't a simple answer to that. On the processor side, If looking at a straight correlation; same die size, exact same architecture; then on a 14nm process we can theoretically have 4 times the power. But its not that simple. cauby 2017 14nm chips won't be cheap. At that time all the other chip making foundries would just be getting to 14nm meaning that yields would be low. Low yields means more expensive chips. The guys making the Chios for Amd for both the PS4/XB1 are yet to start 20nm fabrication. That means we don't see those in consoles till next year at best. 

A much more powerful 14nm console can be made in 2017/18, and by much more I mean like 6-8 times more powerful if they went back to building the CPU and GPU on different dies. But there are too many problems with that kinda design. RROD, YLOD...etc. There are also a lot of developing techs in storage I/o, memory types and bandwidth..etc that are worth waiting out for. 

Well, that is not design issues becaus of seperated CPU and GPU. It was problems with bad cooling design, lead free solder and by meaning of word the hottest consoles ever.
Microprocessors are very effective heaters. Almost all energy you put into them come out as heat.
Now as for die shrinks, shrinking a transistor to the quarter of the size does not mean it will need only a quarter of the energy.
Then there's the clock speed. We had 3.2 GHz for PS360's CPU, now it is 1,75 and 1,6 GHz. Why is that? Raising the clockspeed will increse power consumption and thus heat almost exponentially. There are other side effects as well. Like electron migration, a major issue of Intels Pentium 4 design. Those CPU's had up to 3.8GHz in 2005.

Now we have to feed our components with enough power, cool them and so on. Tough challenges for the actual console design.

All that has to be balanced for a handy nice console design, that is as well not to expensive, probably no one wantts to make losses like in the seventh gen ever again.

PS4 and One are interesting in terms of cooling, PSU and so on by the way. Both designs are siblings in terms of CPU and GPU. But while Sony went with a highly integrated, compact design MS chose a very conservative one. Neither of both is actually bad. But the higher power consumtion and heat go, the more difficult a nice, living room compatible and compact design will be to realize.
And the more expensive components like cooling and power supply get.

In conclusion, it's not about what is technically possible, but what is living room compatible worldwide, not to expensive to sell without major losses and reliable enough to not get a next RROD disaster.

Now there's a final, important point. There can be major steps made even without a die shrink or changing clock speeds. That is something we can see with new processor designs but also with improved designs. Like Nvidias Geforce 5XX series, still a Fermi design, but improved and more efficient than the original design.

Console manufacturers want a not to expensive, living room friendly, reliable design. They want as well a big enough step. Only exception until today was Wii, but it was centered all around new control schemes, something that has only worked once.
Now, if we go for 2019, possible 10nm manufacturing and so on, between 10TFLOP/s and 15TFLOP/s on a GPU heavy design are highly possible, but a giant step like from SD to HD seems extremely unlikely.

Spot on. I don't think we will ever see the kinda leap we had from SD to HD again. Even if under the hood a similar order of magnitude power jump is being used. I mean with a 10Tf-15tf jump, its not like games will suddenly look 10 times better. Resolution will get 4 times higher, ftamerates will average 60fps, lighting will get better.....etc. But it really just amounts to more and more polish. More refinement, this is not a bad thing, its just the nature of the industry we have to accept. 

As far as interface innovation, only place I see it coming is from VR. And even at that, its not like all games will suddenly be better in Vr, it will just cover a certain genre of games. And will be mostly kept optional. No chance in hell Sony or MS bundles a vr headset with their next console. 

As for VR, i actually dont think that it is really something for mass market. But it should at least be far more interesting than 3D on TV's.

Major technological steps with more power: I got somewhat bored by the graphical improvements over the last years. And benefiting from 4K (or 8K) highly depends on screensize/distance ratio. It's nice if you sit two meters from a 65", it actually doesn't matter if you sit 3.5 meters from a 50".
Framerate is good for many genres. But if we get more frames or not depends on the devs. Going with less detail could have given us 60fps in the last gen. Right now devs are again heading for more detail.

The other really interesting stuff is things like softbody physics, that could really improve gameplay.