Recent NVidia cards have a feature called DSR (Dynamic Super Resolution). You can use this to try out higher resolutions even if your current monitor can't cope with it.
D:OS can definitely cope with 4K as long as your graphics card can keep up with it.
Is there a general problem with not many games supporting this kind of widescreen monitor though?
It is not full 4k, its extended 1440p so it do not require a nuclear plant to run.
Most new games and many older support the resoultion , but you got some oddballs like overwatch, homefront, fallout 3/nv/4 (can be fixed with mod),vanishing of ethan carter and many ubisoft/blizzard games do not support it.
Most games that can be modded to fix it and run ok . Sometimes the cutscenes etc get cropped or menus get strange.