By the way, the response is , oddly enough, " How do you do?"

Nobody uses this kind of greeting any more, well for sure maybe some of the older generation do, or maybe some of the younger generation who have been brought up in more upper class environments. That's not to say that people from more working class backgrounds don't use this kind of language, but generally I would say that across the board, this kind of language is a bit old fashioned and unnecessarily formal, even in some formal situations. Of course not everyone would agree with me, it's just in my experience of 42 years I can say I came across this kind of talk maybe only a handful of times.

It's because it's considered formal language and for most American, at least, it's not a phrase we say very often. I can't ever remember saying it, actually :-) Even when I'm being formal I just say "Hello. How are you? Nice to meet you." I shorten it to "Hey! How are ya?" when I'm talking to friends :)

In the US, "How do you do"? Is only used the FIRST time we meet someone in a FORMAL setting. After that we might say Hello or Good Afternoon, etc. This is a common question on italki and a source of much confusion.

People shouldn't be shocked. In the US this is a perfectly acceptable greeting. If I was greeting someone formally in the US I would say "How are you?" and my friends I would say "What's up?"