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.
Thanks. I'll check BENQ if there is some way for it to "remember" its last state. (My old Samsung CRT of 2002 could remember it)