I have always had this hunch that cats take their vomit to the carpet because they don’t want to feel it uncomfortably splatter onto their paws(the way it would on a hard surface like tile).

It would be congruent with a cat’s overall air of arrogant superiority. It’s a bonus for them that they also get to watch their human groan and complain as they stoop to clean it up like the servants they are.