I might have a similar issue with my lg ultra wide monitor as per this video (towards the end)
My solution is to flick the switch at the back on / off otherwise you have to wait for the grey 'no input' screen then wait for the standby light to flash THEN press the one button to wake it.
The 31MU972-B has been working fine on El Cap, all day yesterday and so far this morning. I really think it's a Sierra issue.
On Sierra if I powered off completely, then rebooted but didn't login, then let the Mac sleep, then tried to wake it - the screen would never wake w/out pulling the plug on the Mac and restarting it, no matter what monitor on/off or thunderbolt port dance I did.
This worked the first time I tried it in El Cap. I don't think a day is enough of a sample test for the other random times the screen wouldn't wake up in Sierra but I'll let the thread know if it happens again.
Now I just need to figure out a contingency plan should this system fail that doesn't rely on Apple.