Frankly, I think color temperature is important in all aspects of lighting. As the general public is inching its way toward the use of dimmable fluorescents and LEDs, we do want to look at the color temperature and the CRI (color rendering index). When houses were done with all incandescent light, it was very simple. All of the illumination was the same color and when dimmed, they all became warmer in color. If the house is done in all fluorescents or LEDs, then the coloration and dimming will be constant. It's when you start to mix light sources that you have more inconsistencies … like when you mix cocktails.
When providing indirect illumination, the color temperature of the fluorescents or LEDs should be close in color to those of the other light sources in the space. I personally use dimmable LEDs or fluorescents that are the color of dimmed incandescent (2200K to 2400K) so that when I dim the incandescent lights, they will all feel closer in color temperature at the lower light levels. Now I'm changing out my traditional halogen MR16 lamps with LED versions, but I still add a “warming filter” in front of the lamp to add an amber hue. For closets, garages and laundry rooms, though, I do like my lamps in the 4000K to 5000K range for color matching.