I have this issue too and another related issue. When playing via Steam Link, if the monitor goes to sleep, there's no way to get it to wake up with just a controller. A keyboard or mouse is needed to wake it. I'm on Arch Linux too. In the case of the monitor going to sleep with Steam Link, the link is connected, but it just outputs a black screen.
I have this issue too. It happens on both Arch Linux and Ubuntu MATE on different PCs. The controller in Big Picture doesn't send wake up events like the keyboard/mouse do. It happens both in Big Picture directly at the PC and over the Steam Link. In both cases, once the monitor goes to sleep, you must use the keyboard/mouse to wake it. Note that this is the monitor sleep timeout, not a PC sleep.
Nothing extracted yet.
I'm using steam on ArchLinux with I3 as my WM.
It seems to me that using the controller doesn't send events (to X11).
So the screen goes blank after a while. It would be great if steam would send a event ocassionally to DPMS & Co. so I don't have to reach for the Keyboard if I don't want to.