I have to quibble with that. For starters, there are plenty of displays out there nowadays which do not have an RGB sub-pixel structure. Pretty much all OLED TVs, for example, have RGBW sub-pixels, so there is no point anywhere in the signal chain that the picture is in RGB format.
Second, what do you mean when you say that the pixels “need full-range RGB”? Assuming an 8-bit signal they need to correctly display 220 possible levels of brightness, not 255 levels.
And, while you do go on to say that it’s probably better to let the television do the “conversion”, I don’t think you put enough emphasis on that. Most televisions do all of their processing (e.g. scaling) in YUV space; and it’s quite often the case that an RGB input signal will actually be internally converted to YUV for processing. Supplying a television with RGB will quite likely degrade the eventual picture quality.
Making statements like “the pixels need full-range RGB” makes it sound like, if only you can convert to RGB correctly at source, this will result in optimal image quality; and that is emphatically not true (unless you’re dealing with a PC monitor type display).