I was definitely taught to eat this way, scolded if I didn't put the knife down and return the fork to my right hand, along with when to abandon a piece as inedible, rather than change from eater to butcher. I am pretty sure I was also trained to use the fork to lift food and not to stab at it. It amuses me to hear this called "shoveling" as the intent is to be less crude. I was likewise trained to only dip a spoon away from me, which avoids any impression of shoveling or bailing food towards the face. Also, numerous details about the staging of bread and butter to a bread plate and when to break it by hand and when to take a bite.
My casual adult practices and lost memories would definitely disappoint my maternal ancestors... My mother was from a mixed family of blue-bloods from the US northeast and German immigrants a couple generations removed. She probably married "down" with my father, my inculcation thus diluted. She didn't talk about it much, but I think there was some pressure to conform to those blue blood ways within her extended family. I believe her sister was involved in the Daughters of the American Revolution and was also put through some sort of finishing school when young. I hear an odd echo of that aunt whenever I hear Martha Stewart speak. I remember events with very formal table settings when I was a small child, though I have forgotten many of the procedural details for upwards of 5 utensils per place.
All of this is to say: it is a formal cultural practice at least in parts of the US, not some absence of training. I would also believe it has some origins in a display of disarming, much like a hand-shake and other rituals. I wonder if anyone from the UK can comment on whether there are notable regional or class-based practices and any that seem to match the American method described here. I would expect there were British roots, though it might have died out.
More practically, the US method limits eating to a polite pace. Out of context, European and East Asian eating methods look extremely crude to an American eye, with people shoveling, lapping, and slurping food towards their faces. In context, I of course realize they are culturally expected and my American way would seem odd or perhaps even disdainful.
As an aside, I found it interesting to learn how Thai people use a fork and spoon. They use a spoon in their right hand much like an American uses a fork, except they may keep a fork ready in the left to assist in loading much like a European uses their knife (but with hands reversed). But, if an item needs to be cut, the spoon is suddenly a knife without any hand switching and the fork may control the item as it does in American hands.