Oh boy, napkin math! (not sarcastic at all - I think this kind of ballpark estimate is actually super fun)

A Titan XP/1080 Ti is finally just about enough to push 4K/60Hz with a single card. 16K would be 16 times as many pixels per frame, and 144 Hz is more than twice the refresh rate.

To put that another way, we haven't even started to think about the connector standard that you could gang together to push that many pixels, let alone having a GPU that could actually push them. At this point you are pretty much talking about some kind of lossy compression being involved ("visually lossless" sure is a great euphemism). With lossy compression you might be able to get away with ganging together a couple of whatever DisplayPort 1.5 or 1.6 end up being.

In fact with the end of Dennard scaling there's some fundamental problems with how you would even use a GPU like that as a consumer. Your average (US) household circuit is 120V/15A peak, and can be run at 80% load continuous (12A), which works out to 1440 watts at the wall. With an 80% efficient PSU that works out to 1152 watts inside the case.

A Titan XP/1080 Ti pulls 270 watts at stock clocks [0]. So hypothetically even if you stacked four of them on an interposer you're now pulling 1080 watts inside the case, which is almost your entire circuit capacity. So by a naive calculation (16 times the pixels twice as fast = 32x divided by four GPU dies) we need at least an 8x improvement in overall efficiency before this is viable.

(Four big GP102-sized chips on an interposer is technically possible right now - they only need to be on the interposer where you need interconnect bumps - they can hang off onto a support substrate, and you can have shared memory controllers/HBM2 stacks/etc on the interposer that make this appear to be one big GPU chip instead of SLI/Crossfire. Since the interposer is actually a chip all on its own, some of these auxiliary functions can actually be built into the interposer itself (the "active interposer" concept), with the biggest obstacle being getting the heat out since the interposer has other chips stacked on top of it...)

220V users obviously have things a little easier here (~twice the capacity per circuit). This cuts the overall efficiency improvement necessary down to 4x.

There will also be some efficiency improvements on the software side. For starters we can cut quality a bit (that's 4K/60fps ultra), foveate rendering, and other software magic. Speeds don't scale perfectly negatively with increased resolution so you will get some savings there. Assume some speedup from DX12/Vulkan too.

Oh and since this is 16K/144 Hz per eye I guess there's an implicit assumption here that we can make NVIDIA-style Multi Viewport Rendering work at near-100% efficiency, otherwise that's another factor of (up to) 2x that needs to be accounted for.

So let's say that we need a 4x improvement in overall hardware/software efficiency. Let's say, something like a doubling in GPU throughput-per-watt and to double software efficiency before an absolutely state-of-the-art rig could even feasibly do this task on its own dedicated 220V/15A circuit. And there's a few fairly optimistic assumptions built into that 4x number.

Take your best shot at how long it will take to quadruple efficiency in the post-Dennard era. Let's say 20-30 years, unless there's a massive breakthrough in materials science or optical computing or something.

[0] https://www.techpowerup.com/reviews/NVIDIA/GeForce_GTX_1080_...