I’ve never thought of carpeting a wall but I wouldn’t rule it out.
One major benefit that springs to mind is sound-proofing and reducing “echo”
Now that lots of people have moved from carpet to hardwood flooring or tiles, it could be useful to have something soft on the walls to absorb the sounds. I hate that echoing you hear in a room without carpets or many soft furnishings.
A friend of mine lives in a semi-detached house.
Her neighbours are not particularly noisy and she rarely heard much noise from them over the last 20 years but since the neighbour has refurbished the house last year in a modern “minimalist” style, making the downstairs open plan and laying hardwood flooring throughout, the noise coming through the wall has increased a lot - you can them laughing and parts of conversation - you can even hear them walking across the floor in the living room, hoovering and general living noises sound like they are in the same room as you - even the clatter and clang of saucepans echo from the kitchen at the other side of the house.
I don’t think I could stand living next to that racket.
If I lived there and couldn’t move, I would consider putting some sound insulation on the party walls in my sitting room and 2 of the upstairs bedrooms to reduce the noise - maybe carpet and a layer of sound insulation underneath would be just the ticket.
I’ll suggest it to my friend as an option.
Vacuuming it regularly may be a pain but you can get very light cordless vacuum cleaners now - it could be a great upper body exercise workout!
It would never wear out or get too dirty, like carpet underfoot.