I had to leave before I could write an explanation. The spike is cause by data that goes from super-bright to clipped, and most of it is in the wall, not in the building in the background.
In this photo you’re dealing with the clipped white of the building in the background and the clipped wall lit by the sun. You want to recover the color and texture of the wall and for that highlight reconstruction using color propagation works best, but you also want the clipped white of the building to remain white - you don’t want the white paint to turn any other color. What works well for one does not work well for the other. My PP3 addresses both issues - it recovers the color and texture from the clipped wall using highlight reconstruction with color propagation, and uses Defringe to remove the colorization of the white wall (how did I know to use it? I zoomed in 1:1, noticed purple edges where there shouldn’t be any, and know that Defringe is designed to prevent that - know your tools, read RawPedia). Automatic raw chromatic aberration correction often prevents problems too.