Another cat owner asked me what I thought cats wanted you to do for them when they are yacking up a hairball. This made me think. I know exactly what they would want you to do. That is... nothing.
By instinct, cats are very good at hiding their illness. They try to protect themselves from predators and from feeling or looking vulnerable. The last thing they want is for another animal to see them, sense their vulnerability and attack.
So when your cats are yacking up a hairball they would want you to keep things calm. If there is a lot of hoopla going on in the house - stop. Speak soothingly to your cat but do not approach him. Do not make him feel threatened or vulnerable. Leave him be. Let him feel safe.
Once your cat has regurgitated the hairball and is once again composed, gently and slowly approach. Pet or talk to your cat. If he wants to be left alone, leave him alone - but watch him to ensure that this is a one-time event, that he begins eating and drinking normally soon.
With that being said, I totally understand why you would hope the hairball is an area that is easy to clean. But the question wasn't what you want - the question was what the CAT would want.
What your cat would actually appreciate most is PREVENTING the hairball before it happens. You can do this most effective two ways.