Regarding of signal processing, usually, large part of the energy of an image is on the lower frequencies. When rendering on lower resolutions, we lose some of the higher frequency content. But there are usually few of it.
Mathematically, a 1080p image has kind of 95% of the 4k content. Is 4x less pixels to render for 95% of the content. make the math.
Checkerboarding helps a lot too, id say 98%. Also, the AI solution of DLSS create a 4k image from a lower resolution, letting the AI complete the higher frequency content post rendering, 99.9% maybe.
Even without those techniques, Id rather have a 1080p image with a good AA than spend money for 4x more power on computer resources for a 5% gain.