The resolution question in wallpapers is more contextual than most discussions suggest. Whether 4K matters depends on your display, the type of image, and how closely you sit to the screen.
Resolution matters most for: highly detailed photographs with fine textures (stone, fabric, foliage), architectural images with precise geometric elements, and text-containing images. These image types have detail at the pixel level that lower resolutions blur.
Resolution matters less for: simple gradients, abstract art with large shapes, heavily out-of-focus (bokeh) photographs, and solid color backgrounds. A gradient looks identical at 1080p and 4K because it has no fine pixel-level detail to preserve.
Pixel density (PPI — pixels per inch) is the actual relevant metric, not raw resolution. A 24-inch 1080p monitor has a PPI of approximately 92, which is below the threshold where individual pixels become invisible at typical viewing distances. A 27-inch 1440p monitor has PPI of approximately 109. A 15-inch MacBook Pro has PPI of 254. The same "4K" wallpaper looks sharper on the MacBook because the pixels are denser.
For Retina (HiDPI) displays: always use the highest available resolution. Apple's Retina displays literally double the pixel count for the same logical resolution — a 2560×1600 display on a MacBook actually renders at 5120×3200 internally. Using anything below 5K source images on these displays wastes the display's capability.
File size vs visual quality: on modern storage (SSD with surplus space), file size is rarely a meaningful constraint. Download 4K files even if your current display is 1080p — you may upgrade in the future, and the file is your permanent copy.