DisplayPort 1.2 can do it, if the monitor pretends it's two half-size monitors next to each other. This causes major problems for OSes, though I did eventually manage to work around it on Linux. (On an nVidia card, enable Xinerama. Due to a bug, this turns Xinerama and RandR off, making the window manager think you only have one monitor. Perfection.)
HDMI 1.4 can do it, but only at 30Hz, which is ugly. It's actually not unusable, but you'll be aware of what's going on.
As for the resolution issue: you're still not getting very good density. Your phone can do 440ppi. The Chromebook Pixel is 240ppi. 32" at 4k is 140ppi. Mind you, it looks great at 200%, but things are a little big. (I ended up liking this and my normal monitors now run at 125%.)
You really want 8K for a big monitor.
You also want 120Hz refresh, if only so that movies play each frame at a constant speed. 24 doesn't divide 60 (or 30!), but it does divide 120.
So until there is some transport layer that can do 8K at 120Hz, we're taking a step backwards. (4K at 120Hz is fine for TVs, though. Perhaps even HD is enough there.)