More and more I encounter "across the globe" when I would expect "around the globe": "We have merchandise from across the globe." My feeling is that it started as a Britishism, and I thought it quaint; but now that it seems to have moved to the US it seems wrong, and two-dimensional, despite "globe". Does anyone else even care?Â
It does sound flat. Â Or sounds like going through the molten core.
And even if you accept the 2-dimensional nature of the surface, there is the problem of lack of boundaries. Â ( Across America sounds natural because there are the 2 beaches on 2 sides.)
But John Lennon clearly doesnt bother with matters of  boundaries or dimensions: his words fly across the universe.
I have no feel about the Britishism part though.
I'm willing to cut Lennon some slack, a) because of his English heritage; and b) because, in my book, poets and lyricists get an exemption, especially Beatalic ones.
I've always used "around" rather than "across" when speaking of the planet as a whole. Every definition of "across" I've come across relates the (spatial) meaning as "from one side to the other." As Robert points out, that meaning works fine for "across America" or even "across the continent" because there are indeed opposite sides. But it doesn't sound right to my ears to say "across the globe" ... even "across the map" sounds wrong, perhaps because the two sides aren't really physically opposite boundaries.
No idea if it stems from "British quaintness" but check out this Ngram. While you're there, switch the corpus to British English and re-run the search. You see a slight uptick in the use of "across" but nothing really significant. And personally, I have not heard/seen any increase in the use of "across" in this context.
Well, I was going to add this as an edit to my previous post but that function appears to be disabled now.
It occurred to me that the uptick in usage of "across the globe" (starting in the 1980s) might be due to its usage on some popular TV show of that period. I seem to recall some show starting with "... across the globe" in a booming male voice. Bringing you news from across the globe? Incredible adventures from across the globe? Heartwarming stories from across the globe? Not sure what the first part was, but pretty sure it ended with "... across the globe." From there it just emerged as a meme. Maybe some other forum member has a better memory of the 80s. 🙂