Most people have an expectation that residential lighting is on the "warm" (low color temperature!) side. I have a lot of Hue and Sengled bulbs in the house which are tunable and my son complains that they look "harsh" when they are set to a high color temperature. Myself I do art projects that require making fine sensory distinctions and it clear to me that I can do that better with more blue light.
I've seen high-quality incandescent bulbs however that do very well on my tests despite being "warm" but I think a lot of people like using daylight from out the north window for evaluating prints and it was was a revolution a few decades back when art museums realized that higher color temperature lights brought out colors better.
The TV is a good example because the light from TV is transmitted light, like a stained glass window. The TV can create the widest range of perceptual experience if it has R, G and B colors that are precise spectral lines.
If I'm looking at color prints in a book or on the wall that is reflective light and it is dependent on the spectrum of the room. My main TV room has RGB Hue lights that can simulate "warm" or "cold" light but also specific colors. I think 100% green is the ideal light for hot summer days because a full spectrum is also coming in the windows and it gives the most light for the minimum amount of heat. I also find other colors fun sometimes. The guest room that also has a TV has sengled lights that can be tuned from cool to warm.
RGB lights that can produce saturated colors are not going to render reflective colors so well, see
Personally I like high color temperature light but with the system we have we can have it any way we like. If I really need accurate color rendition I bring in high-performing spot incandescent and maybe someday LEDs. My work is all "born digital" so I spend at least 80% of my time looking at screens and looking at prints, handling paper and such is a small but essential fraction of that.
What I really gotta do though is set my system up so it can vary the room color together with what's on TV, that ought to be cool.
I've seen high-quality incandescent bulbs however that do very well on my tests despite being "warm" but I think a lot of people like using daylight from out the north window for evaluating prints and it was was a revolution a few decades back when art museums realized that higher color temperature lights brought out colors better.