In a scene lit overwhelmingly by one approximately Planckian light source, the white point is the color of the closest Planckian light source.

If the light source is not approximately Planckian, or if multiple illuminants have different temperatures, a white point is not defined.

So in this case there is no sensible white point since there is no illuminant right?

I'm not sure what case we're talking about but if it serves visible light it is an illuminant.

Deep space photos - I don’t think there is an illuminant at all

As an aside, I think you are referring to black body sources, which is described by Planck's law. Stars dgaf about color spaces of computer monitors. They are relatively close to black bodies as thermal emitters, though, at least on main sequence and +/- some spectral lines.

We physicists never use the term Planckian for thermal black bodies. That adjective would be used in quantum mechanics, though, for very small things.

Yes, I am. Planckian radiation is the term of art in color science, prescribed by its standards body, the CIE. https://files.cie.co.at/CIE_TN_013_2022.pdf

To understand what I mean by "closest Planckian light source" see https://en.wikipedia.org/wiki/Planckian_locus

Don't forget my fav, the humble reflection nebula. Of course there are always emissive stars in the background of any image of one so the point is moot. But still, there are a few hundred! :D

I know nothing about astro-anything so forgive my ignorance, but what light source would a nebula be reflecting? Is it meaningfully distinct for each nebula?

I'm no expert either, I just think they look neat. But from what I know it's primarily the nearby star or star cluster illuminating them, so yes it'd be distinct. Also there are mixed emission and reflection nebulae so technically I suppose they reflect some of the light from the emissive portions, though I'm sure it's a tiny contribution.