These guys live in a different world from you and me.
They promote speaker cable and stands the price of a small car, SCART leads that are worth more than the average HiFi system etc etc.
If you are in your twenties, are teetotal, have perfect hearing and have a sound proof room, you just might - maybe hear a difference.
It's the same with TV pictures - using good RGB or component sources will give you great pictures on a good TV.
But a mains filter will may not one jot of difference unless there is a specific local problem with the mains supply.
The TV's transformer and control systems sort out most routine issues unless the voltage falls below 220 volts.
Now a spike protector is a different thing entirely and I would recommend them - less than £10 if you shop around.
As for me with traffic noise outside, the phone going, my PC running and a glass of red wine just poured - I'll take my chances on a cheap lead and power supply!