Can't turn off the computer using solely the Power button

This is a gripe I have had with the way Unity responds to pressing the hardware Power On/Off key (typically found on the front of desktop computer case or somewhere near by keyboard on a laptop).

The problem is that there is no way to turn off the computer by pressing the key as the press event only brings up Unity choice overlay (Shutdown/Restart/Suspend/Hibernate) but the user is required to use mouse to click on the icon to take the action (maybe there's a keyboard way too). In previous versions of Ubuntu, there was a timer ticking that would invoke shutdown if no icon was selected. I believe the other desktop OS (MS Win, Apple OS) have the same timed default behavior. At some point a year or two ago the overlay was redone for Unity and the timeout shutdown had disappeared.

This is a major pain for me because there are two scenarios where I am forced to "hard" power off with the accompanying chance of data loss and other issues.

Scenario 1: My computer is on a UPS, the monitor is not (too much load for the UPS). When the power goes out, and the UPS starts running out of juice, I want to safely shutdown the OS before UPS gives in. I can't.

Scenario 2: Something just had happened to my input devices (keyboard and mouse) and I lost the control, but the OS was happily running, so pressing power button brought up the overlay but I couldn't choose anything.

PLEASE, return default shutdown action to the overlay!