Perhaps I've misused my terms, but your inspiration images that you have linked are quite grungy grey colours, some of which do in fact appear to have cooler undertones.
Furthermore, upon closer inspection, a few of those inspiration images can be satisfactorily recreated using our existing palettes. You yourself provided a screenshot of Seri's work which wonderfully executes the palette seen in a few of your images.
https://imgur.com/g6ZlKWu
If we consider potential reasons for King's Landing's stone variety, we can surmise that the dun and orange bricks are made from clay, the grey palette is natural stone, and the Stormlands palette being some kind of local sandstone, perhaps from the moat digging or from nearby rivers. It may also be that Stormlands is used as an aesthetic choice to convey squalor and poverty in areas of deprivation as per canon.
Oldtown, however, has two types of stone, golden reach, and pink reach. The golden reach coming from the mountains in the east, south-east, and the pink reach from the north. Where would this third 'dark reach' palette come from? Oldtown is a relatively well kept city in comparison to King's Landing, which is notorious for its poverty and overall dirtiness. Therefore, a darker, grungy palette that could be justified as That is not to say Oldtown is *not* dirty, but that in general it is more looked after.
I want to reiterate the impracticality of adding an entire palette for a region that is largely completed. That's not to say I don't think we should have a variety of palettes, however, we must understand the implications of bringing this to fruition. If implemented, regions of the southern Reach would need to be retrofited with the palette to ensure regional consistency and demonstrate adequate transition of stone types. Moreover, it would provide grounds for redos in the northern Stormlands, which hold complete projects. The implementation of this palette could set a precedent for redoing builds because they are outdated by a new palette that we bring in.
Lastly, I'd like to remind you that this is an open forum thread, and there's no call for attitude over a simple misunderstanding.