There are so many misconceptions about language in one short paragraph, I'm not sure where to start.
But:
US English tends to be generally more formal (I have the feeling you won't like that, but there you go, it is what it is) than much British English.
Phrasal Verbs (coming from Norse languages via Middle English) are informal. (Most commonly used phrasal verbs have almost synonyms which derive from Latin languages- long considered "superior" or "better" and infinitely more formal than words derived from Norse languages.
So: Phrasal verbs aren't used in US English as much as in British English due to the face that US English tends to be more formal in tone.
The reason why these words/phrases are jarring to you in "modern" English is that "modern" English has changed far more, and far more quickly than US English. ("swap out" being a perfect case in point- it has a very specific technological meaning- nothing to do with "ordinary" swapping. US English (with more technology based industries than the UK) saw that British phrasal verb and thought, oh, this explains perfectly what we do, we'll have this one.
All of which leads to people who don't know much about language a) thinking the particle is redundant b) not understanding the meaning of the verb and so applying it incorrectly just to mean "swap" c) complaining about Americanisms d) thinking that US English is a "contagion" influencing British English when it's almost always the other way round.