I have this same issue, but it doesn't seem to be do-not-disturb. I do keep that on a lot, but I tried even with it off and the screen still doesn't wake for anything. The same thing happens for alarms, I can't deal with them from the lock screen I have to unlock the phone and go to clock or get there from the notification...
I did change the default calling app to exDialer, and also changed the clock to google's clock app, but all notifications are enabled for those apps.
Any other reasons this could happen?