Mark Lloyd writes:

The IR receiver in the TV does have to be active, to be able to
respond to an ON command from a remote control. Some TVs have clocks
in them, another need for continuous power.

Most CRT-based TVs from the last several decades keep the heaters in the
CRT somewhat warm when the TV is "off". It speeds warmup and also
reduces thermal shock to the heater.

My TV also loses its channel programming when the power is off. That
might be less common these days, since flash RAM is cheap.

Dave