These are the facts I have so far on this issue. Its possible some of them only apply to my system.
1) Apple is aware of the problem. I have spoken to them and they are working on the issue as others also reported. It seems they are trying to gather system diagnostics of iMacs in their broken states. I have no idea how much progress they've made but I do know they're still trying to gather as much as info as they can on the issue. I was able to provide them with such a diagnostics file while my iMac screen would not turn on.
2) The problem is intermittent. I have seen it fail in just 30 seconds. I’ve also seen it not fail for over a day with several successful wake ups.
3) When the iMac screen fails to wake up, sometimes the external monitor comes on, sometimes it doesn’t. I have had instances where the iMac screen does not wake up but the external monitor does. But I’ve also had instances where neither turned on but I know the system was actually awake.
2) Resetting NVRAM/SMC doesn’t help. Though it may be a very short term fix. Hard to tell due to the intermittent nature of the issue.
3) Turning off external monitor before going to sleep is a workaround. Then turn it back on after wake up. Of course, unplugging external monitor is also a workaround.
4) The issue definitely started right after updating to macOS 10.12.4.
5) I did attempt a fresh install on my iMac and then went straight to 10.12.4 without installing any other software or even logging into iCloud. The issue still occurred.