The second impact of the Kodi desktop resolution is how media is scaled. If "Adjust Refresh" is not enabled, Kodi will scale all media played up or down to the desktop resolution and refresh rate, which by default is 1080p @ 60 fps. Scaling SD and 720p media up to 1080p while adding extra frames to match 60fps is handled well, as Kodi simply needs to duplicate frames to reach the higher fps rate, and the simple scaling algorithms Kodi uses to reduce artefacts in the upscaled image move smaller amounts of data in/out of memory. Hardware as low-spec as the first generation
Raspberry Pi can normally manage this well.
Scaling SD and 1080p media to 4K is a literally bigger challenge. Frame sizes for 4K media are 4x the size of 1080p so the amount of data being processed in/out of memory increases and the CPU resources needed also increase. Scaling 4K to 1080p is a larger challenge again. Source 4K media has huge frame sizes and sophisticated (down)scaling algorithms are required to create a lossy image without massive visual artefacts.