it won't even be a slow decline. Like its common name implies, cottonwood, it is a light wood and doesn't compartmentalize wounds well. In short order it'll start rotting out from the cuts down. The hideous new growth will be super weakly attached.
In a year it will be close to the same size it is now, but full of tall new growth growing from rotten stem cuts. It'll sucker out around the base. In another year or so those new branches will start breaking and falling out.
I don't like any trees in the popular family, their weak, rooty, and suck up vast amounts of water. Remove it and plant something else, but topping one is just bad on top of bad. At lest cottonwoods are nice to look at, topping will take that one good thing its got going for it away.
We suppose to be the experts, tell him the truth and set em straight. Does that ho tell his gardener how to mow his yard? Well he shouldn't be telling his arborist how to handle trees.
I know some times you need the job to make it, but at lest tell the ho the truth and how detrimental it be to the tree. He the one who'll have to look at that ugly sucker every day. Beastmaster