If we are going to go into detail, then let's mention that the fact that you've matched the black-body line in the CIE color space does not mean that you've matched the black-body spectrum. Which means that you can have a light that looks "white" to an observer through a lampshade, but which distorts the colors of the surroundings (since nobody matches those to where they need to be in CIE 1931). This is exactly the problem with casual observation - "light looks the same" is not enough.

Anyway, all I meant to say is that the smooth spectrum of incandescents is what people like to light their homes. It allows natural perception of colors of the surroundings. The high-tech approaches to getting there are a) not as good, b) expensive, c) not so good for the environment, once you add it all up. Now, for specialized applications, I am sure that LEDs are wonderful compared to complex filters on incandescents, but that's not the product we are looking at.