This would be a function of the monitor.
Your wall switch shuts off teh AC. When restored, the monitor does not remember its last state so stays off.
The computer does or has a BIOS setting to enable a last state reset so it can be set to turn on.
Only thing i can think of is to connect the monitor to a different AC outlet so that it always stays on.
It will go in to a low power mode if no video from the computer is present.
When you flip the switch, just the computer will turn on.