[dspeyer]

First thought:

The usual pattern is that only one X chromosome gets transcribed in any given cell.[1] This keeps the dosage of all those proteins correct. Otherwise there would need to be a separate set of dosage controls for XX and XY people.

The inactivation occurs pretty early in life, and when cells replicate they keep the inactivation. This results in macroscopic regions of the body with consistent inactivation. Usually this isn't noticeable, but in cats coat pigment is on the X chromosome, and heterozygous cats often show "tortoiseshell" or "calico" coloring. The patches of contiguous color there are larger than a retina.

So it seems entirely likely that all the cells in a human woman's retina would use the same X chromosome.

On the other hand, that predicts half of het women would be colorblind, which isn't observed. So maybe not so simple...

I have a second thought about downstream neural hookups and the mechanisms for those, but it'll have to wait for later.

[1] https://en.wikipedia.org/wiki/X-inactivation

[xerula]

The article explains X-inactivation, and it doesn't play the role you think here: both copies are broadly equally expressed among retinal cells. Also even if all cells in a retina used the same X-chromosome copy it doesn't predict color-blindness, since we would still have a trichromatic system.

The answer to the question posed by the title is simply that all mutant fourth cone types are not created equal. Most have a spectral response curve similar enough to an existing type not to make a real difference; a few have peak responses more squarely in-between those of the usual trichromat photopigments, allowing more finely graded color perception. (The article takes its time getting round to explaining this, but it's all there.)