Quarior, by post-editing the picture you'll loose tiny features of the scene.
I have the same display definition as you. In order to make a full HD screenshot (1920x1080) I compose my scene by placing the camera where I want, then I open the Display menu, in Window Mode / Windowed (I always use SE in maximized window mode) I change the window size and Apply.
Hit F11, and you'll have the desired screenshot.
As for the requirements, I guess since Full HD definition is universally achieved in PC and TV displays nowadays, using minor resolutions it could be a not so good representation of SE rendering capability.
Moreover, it seems the market of bigger display resolutions (4K) is steadily growing this year, so we'll all go there eventually, with a standard resolution of 3840x2160.
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My mods - My specs: Asus x555ub - cpu i5-6200u, ram 4gb, gpu nvidia geforce 940m 2gb vram