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.
I’d be more inclined to say they know it’s smelly waste and want a soft surface to bury it in.
Which begs the question of why they don’t go for the litterbox, but mine do always try to bury it right away.
One of my cats actually does puke in the litter box and buries it. I wish she would teach the others.
Considering my cat has never once hit the tile despite 80% of the house having hard surfaces, I totally buy this.
Sorry for off topic: If your cat pukes very often, please get her liver values checked.
How often is too often?
If a cat does not just throw up hairballs sometimes but pukes out the cat-food regularly, directly or soon after eating. Then it is too much. Often people think their cat is just eating too fast and throws up because of it. However this behavior can also point to liver insufficiency.
