Now, Control–Option–Command–F19 works with the external keyboard and shuts down the computer. This won't work well on the limited internal keyboard, but for the external wired keyboard I set up one of the useless function keys (F19) as the Eject button. I did, however, find that Karabiner Elements does allow another key to be remapped as Eject. When I disable Karabiner, the shutdown shortcut works normally. Goto System Preferences > Keyboard under the tab Shortcuts select App Shortcuts in the left column and then click the plus button.

There is a simpler solution, without the need for third party tools. It seems that, at least on my machine, the key remapping program Karabiner and the Sierra-compatible version Karabiner Elements causes the Eject button to not register at all. I have hot corners active, but have three screens connected to my MacBook Pro, and that is quite a distance to travel. Each time you press Tab, you move through a list of apps, but you can also tap the Q key. UPDATE: I found that the standard Control–Option–Command–Media Eject does indeed work with Sierra. Control+Esc (+) or Control+Eject (+): Display a dialog asking whether you want to restart, sleep, or shut down. To switch quickly between apps on a Mac, you can hold down the Command key and repeatedly tap the Tab one. I assume Apple added the additional shortcut for newer devices that don't have optical drives and eject buttons, but they neglected to maintain the eject-button shortcut for the older machines within the Sierra update. I tried the power-button shortcut on my MacBook Pro Mid 2012 with macOS Sierra 10.12.4 and it worked similar to the old eject-button shortcut (maybe a little slower, but that could be the new OS).

According to Apple Support, there are two shortcuts for shutdown:

Shortcut to shutdown macbook pro