Yes, and I already noted that things like standing close enough to an object that it more than fills the viewport will potentially use higher resolution textures. At the same time, there will be lots of stuff (think of all the little objects like grass and detail textures) that basically won't render at more than a few hundred pixels. Most likely the artists / developers don't even package 1K textures for things like that.This happens on a per-pixel basis, often along with interpolating between the two resolutions on either side, so you don't get a hard edge at the transition from one texture resolution to another.
No, textures are often far larger than individual polygons. Even then, if I use a texture map for a wall, and the wall is 20 feet high, then when I'm standing next to it what's filling my viewport is actually just a rather small subset of the entire texture.
That's obviously a simplistic example, but it illustrates the point that 4k textures aren't necessarily a waste, even at 1080p. It all depends on how the texture is used.
It would probably make a good article to compare screenshots of a few games vs. different texture resolutions, to actually test how noticeable the difference is.
I have done an article on this subject. I've also included screenshots at various settings in this article, though I didn't take the time to only change texture quality. I've done that in individual game benchmarking articles though (Diablo IV, Dead Island 2, Star Wars Jedi: Survivor, Lord of the Rings: Gollum, and Redfall most recently).
I haven't tried to suss out whether those games are using 4K textures or 2K textures, but even at 4K resolution, turning down texture settings from max to min tends to only affect closer objects, as you'd expect from mipmapping. And let's not even get into the bit about TAA blurring things to try to eliminate jaggies, so that all the benefits from those ultra high resolution textures are wiped out.
There are always edge scenarios where you can make a game in such a way that using higher resolutions textures makes sense. In fact, one option is to use a single 8K texture that has lots of sub-textures. It could contain 64 1K textures, or 256 512x512 textures. Or it could be for a sky or space map, where only a small section of that large texture would normally be visible on screen at any time. But that's not what we're talking about.
I'm talking about a typical game like The Last of Us, Part 1, where there are lots of small surfaces in any given frame, and very few of those will use more than a 512x512 texture size with a standard mipmapping implementation.
[And I also need to mention here that modern games don't use a single texture for a single polygon. You'll often have a high resolution texture that wraps around hundreds of polygons. But the point still stands that if the wrapped object only covers say a 500x1000 area of the monitor at 1080p — like a standing character at relatively close distance — wrapping that object with a 4096x4096 versus a 2048x2048 versus a 1024x1024 texture will typically result in nearly the same final rendered output.]