

For the resolution of the texture to need to be doubled along each axis, you could either have a monitor with twice the resolution, or you could be half the distance away. Most of the time games will let you get closer to objects than their texture resolution looks good for. So 4k textures still give an improvement even on a 1080p monitor.
Texture resolution is chosen on a case by case basis, objects that the player will usually be very close to have higher resolution textures, and ones that are impossible to approach can use lower resolution.
The only costs to including higher resolution textures are artist time and (usually) disk space. Artist time is outsourced to countries with cheap labor (Philippines, Indonesia, etc) and apparently no-one cares about disk space.
The advantage of making your own engine is that you can specialize for your specific gameplay.