Seems you didn't get my point:

Says the diagram in the OP, the EM spectrum of a 5800K star, which clearly shows a peak within the visible spectrum in the blue band, and a significant (25% or so) drop off by the time it gets to the red band. Those aren’t relatively equal.

Then show me an EM spectrum of this mythical "white light" temperature. No matter what temperature you choose, they all have different drop-offs at different frequencies, look again at this graph I linked to before:

The function isn't even symmetrical, so even if you chose one with the peak in the very middle of the visible spectrum, you'd still get different drop-offs in the blue band and in the red band. So how do you choose which temperature is this perfect white? I'll tell you how you did, you just chose one that looked white to you. You don't like 5800K because it looks blue to you. But it only looks blue in certain context! And there's more, did you know that at lower luminance level, your neutral white will seem more blue?.

Additionally, you don't need the full continuous spectrum to produce the "same" white. You can just combine single RGB wavelengths to get white for example. In fact, that's exactly what we're talking about as we're presumably both looking at the image on RGB screens. But you run into the same problem, because there's no single definition of what exact wavelength red, green or blue is, nor what their relative power should be to produce "neutral" white. But of course this "RGB white" only looks white to humans, some animals would see a different color from the full spectral white.

I am talking about what color it is

But color is perception and only that. You can talk about temperatures and wavelengths but from a physics point of view they're just that - temperatures and wavelengths, not colors! When you go shopping for a laser, you buy a 450 nm or 473 nm or 488 nm laser. You don't buy "blue laser" because all these three numbers are "blue".

Color (American English) or colour (Commonwealth English) is the visual perception based on the electromagnetic spectrum. Though color is not an inherent property of matter, color perception is related to an object's light absorption, reflection, emission spectra and interference.

(...)

Most light sources emit light at many different wavelengths; a source's spectrum is a distribution giving its intensity at each wavelength. Although the spectrum of light arriving at the eye from a given direction determines the color sensation in that direction, there are many more possible spectral combinations than color sensations. In fact, one may formally define a color as a class of spectra that give rise to the same color sensation, although such classes would vary widely among different species, and to a lesser extent among individuals within the same species. In each such class, the members are called metamers of the color in question. This effect can be visualized by comparing the light sources' spectral power distributions and the resulting colors.

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