Anyone that has applied dyes knows the color of the item you are applying them to effects the color. Which can be aggravating. You find a dye just the right shade, apply it, and at best it tints. At worst it becomes a completely different color.
I’d like to suggest a color wash dye. Not so much turn the item white, just lighten it several shades so the color is more true to the dye when applied.
This would be nice, however I’m not sure how easily it can be achieved. Considering textures play a part in the shade of an item. However, you’re right, it would be a closer match than just doing it the way it is currently like it’s a taking on the shade value of the piece in addition to the color.