Technically this is a boring modification, but I suppose this feature was too expensive to put into TV sets in cabinets with doors. "Finished watching TV? Just shut the doors and the set turns itself off! And tomorrow, when you want to watch TV again, just open the doors and the set turns on!" It does sound like a boring feature...
Anyway, using a "normally closed" click switch I got out of a microwave oven, I installed this feature in a console audio system. The insert in the picture shows some sheet plastic I formed to act as a cover.
Here the powerline wires are routed to the back of the console. For a TV with sideway opening doors you'd probably use some sort of mechanical arrangement to have a rod that passes thru a hole to then activate the switch.