I've just replaced an LCD TV I'd had for some six or seven years. This had a separate power supply unit (PSU) but was switched off at the TV so that the PSU was left on all the time. (I did unplug the PSU when I was away for any length of time.) The PSU never got more than slightly warm when the TV was in use, and seems to be have well-engineered. I did ensure it was always in 'free air' and never covered by anything.
My new TV, also an LCD one, has the PSU built in and so is directly connected to the mains. Interestingly the 'On/Off' switch is clearly a low-voltage push-button, not a mains switch, and so somehow turns the PSU on and off without direct mains interruption.
The safety instructions concentrate on installing the TV so that the set does not overheat due to lack of ventilation. They only recommend disconnecting from the mains if the set is not to be used for several days, or if you want to isolate the set completely or when cleaning it or installing/disconnecting AV cables.
Very curiously the instructions also suggest that the mains plug is unpluged to ".....clean it regularly. If the plug is covered with dust and picks up moisture, its insulation may deteriorate, which could result in a fire."
Now that's an instruction I've never seen before!