let us dye the red sash

Yeah. There are tons of textile deco options already in the game that would be dyable. Many are tile-type. Cloth bolt, blanket, rugs, etc, could all be made into cloth tiles.

Upholstered tiles are one of those rare patterns that have popped up from time to time in the real world of interior design. They date back to the dark ages. They are considered beautiful and eccentric, but never made popularity due to durability issues and difficulty of repair/replacement. This makes them perfect for SOTA interior decor where durability is not a concern, and middle ages eccentric design is preferred, and durability of floor materials is not an issue.

As of NPC buildings, I could see them being used as an alchemist's bedroom decor. I could also see them as used in the bedroom of alchemists and other eccentric individuals.

They should also make ceramic tiles you can dye for a more conventional alternative. Once dying wood and stone items is available they could make it so you can dye wood tiles as well. Wood and stone do not display dye in the same manner as cloth and ceramic, this means a shader must be applied to make them appear properly, as a simple single color transparency tint won't do the job right.

edit: p.s. simply put we all would like more deco that we can dye for color changes!