question 1 - is this needlessly complicated?
can this be achieved in a simpler way?
Question 2 - is it going to be prone to failure?
does this have any weaknesses?
Question 3 - has it been done this way before already?
does an existing product already do this?
the answer to the first question is likely yes. could we get by doing something simpler, absolutely... if you can press and hold down the "power button" on the display and apply power to it, and it turns on... it will turn on when the switch contacts has a wire bridge or solder blob across it. if it doesn't and only turns on after you RELEASE the button, you can typically put a 100 or 200uf capacitor across the power button to act as a dead short (as capacitors when discharged have nearly no resistance, but once the capacitor charges up, it acts "open circuit") emulating a button "press".
the answer to the second question is also yes. LED emitters can go bad, Arduinos can crash and become unresponsive. it's going to require another set of wires to power and another set to operate the LED. there will be a bunch of futzing around with timing and whatnot.
the answer to the third question is likely no... as typically monitors used in arcade cabinets, are powered on and off with the cabinet power... so such a thing is not required.
i mean, i havent read your other posts or anything, but if you want to just make a big microcontroller project out of it just to do it, give 'er beans...but it's not really necessary... or really required.