Boxes like that are on 24 hours a day. They do not have an off state, how else are they going to be able to record, update the guide, and other updates.

If the factory remote has a power button, this usually just turns the video output on & off. Again, the box itself stays on 24 hours a day - it has to.

In a system design, there is rarely ever a need to even turn the display output on or off either. Commands are sent to just turn the video display itself on & off and any related audio equipment.