I finally got this persistent problem fixed (2010 Mac Pro had downloaded but did not install Safari/Security update, then afterwards would not shutdown or reboot normally, had to be turned off from the power button). Reset PRAM, SMC, which did not help. Unplugged peripherals, extra internal and external drives, USB devices and extra PCI cards (USB 3, mSATA drives) -- no help. Safe boot worked, but did not solve the problem. Booting from a USB installation of High Sierra worked fine, and would shutdown normally, but problem continued with normal boot.
1. Forced the software updates via Terminal (sudo softwareupdate -i -a --verbose). Updates (Safari and Security) installed successfully, still did not solve the problem.
2. Reinstalled High Sierra from a USB installer. This also did not solve the problem.
Finally, did the following from Terminal (aka "shotgun approach"):
1. rm -rf ~/Library/Caches/*
2. sudo /System/Library/Frameworks/CoreServices.framework/Frameworks/LaunchServices.fra mework/Support/lsregister -kill -seed -lint -r -f -v -dump -domain local -domain system -domain user -domain network
3. killall Dock
4. sudo mdutil -E /
Success! System shutdown worked normally again. I ended up installing Mojave afterwards anyway, but had wanted to solve the problem first, particularly before doing the required firmware updates (requiring reboots) for my Mac Pro.
Hope this helps anyone else experiencing similar issues.