No, Midsomermurderess, declawing is certainly not "very common" in America. I'm American, and I don't know anybody who had a declawed pet, and declawing is considered cruel and disgusting by most people (I'm from Massachusetts, by the way). Declawing is something that I associate with trailer parks and Honey Boo Boo and ignorant people who chain smoke and feed their kids mac and cheese for dinner: NOT something that educated, civilized people do, and CERTAINLY not something that vets "push" at people. Most vets do NOT declaw.
Also, I have never heard of someone having a cat's voice box removed. That is crazy. I don't believe that any vet would agree to do this. If your vet has heard of an American doing this, it must have been a freak one-off by a deranged individual.
I have two cats, and neither of them is declawed or de-voice boxed. Although now that I live in Europe, people keep asking if my cats ARE declawed, simply because I am American.
The uninformed anti-American idiocy is unbelievable. Voice box, indeed!
(By the way, there are some common British customs regarding horse care that most Americans find abusive and hard to believe).