As far as I'm concerned ME-equipped NICs should unconditionally be behind VPNs, but the AMT functionality itself is really cool. Even the 10+ year old machines that don't support VNC let you remotely hit CTRL+ALT+DEL, issue an ACPI shutdown, perform a hard reset (equivalent to hitting the reset button on 486-era boxen), etc. So basically you can do either soft or hard shutdowns or reboots. Quite granular.
I actually used the hard-reset functionality while playing around with Linux early boot on a laptop a few years ago. Rebuild initramfs (loaded via PXE), use `curl` to hit AMT reset endpoint. Very cool.