I think you two missed the last 20 years of IT improvements. Pushing (briefly) the power button does a CLEAN shutdown since the introduction of ACPI, you can use it since Win98SE if installed in ACPI mode, and even since WinNT4 if properly configured. The same applies to Linux as well, and to any other OS which is ACPI compliant.
To put this precisely: What happens if you press the Power button shortly once can be configured in Power options (even separated by On Battery and On AC Power). The ACPI signal isn't Shutdown-only, but universal. There is Shutdown, Hybrid Sleep, Hibernate, or even Nothing at all. Holding the Power button down for more than 4 seconds is hardcoded and done by hardware, the PSU will cut the power (as the mainboard might be stuck and not repond). The reason is that many systems do not have a Reset button. Preferred way of doing an emergency shutdown, many devices and OS support it (although the time to press varies).