Because the server is in a school of Burmese refugees in Thailand. Nobody knows anything much about computers here, so I try to make things as simple as possible. The office lady just used to hold down the button until it powered off...
There is no screen or keyboard on the server.
Right now I have taught them the server manager way of shutting down, but it's cumbersome having to log on to a PC, start a browser, etc.
"Shutdown now" actually goes into single-user mode. You need to use "poweroff".
Thanks to all the hints above I've re-visited the BIOS setup. I was right about the power button config, but I had turned ACPI off in the BIOS. Turning it on fixed it. (I'm sure I've tried that before and it didn't work, but maybe my memory just fails me.)