There will be a new background refresh that will work exactly as you mentioned.
I'm not sure when exactly, but it's planned.
Until it's done, you can at least tweak one value - in Options page / Thumbnails / "Default virtual page width". By default it's 1280 - like old notebook screens. You can try to increase it to 1920 - but I'm not sure if it's gonna be better (not a lot of webs is properly optimized for FullHD).