I think to a large degree the original examples and the premise of the thread are kind of bogus.

School Yard, vs Playgound? Where I grew up the school grounds were not fenced in. There was a parking area, the kids played where there were no cars parked and between the primary and elementary school buildings. The playground was a mile away in the park, next to the soft ball field.

And much as we were proud of our Imperial British heritage, we called the School Grounds, the school grounds and the playground the playgound.

Like wise, girls used to skip and they used to jump rope. There were ways to jump rope without skipping. They certainly would skip without a rope. Skipping with a rope was called skipping rope, often shortened to "skipping."

"Out of bounds" and "Off Limits" do not mean exactly the same thing. Americans are very familiar with the term "Out of Bounds" from football meaning not within the field of play. "Off Limits" is something posted on military installations meaning "authorized personnel only" Since both are used as metaphors and neither are particularly American or British aren't both fairly used?

The English speaking community is connected world wide in media and travel. The users of the language an the influencers are no longer exclusively on a couple of tiny islands. The main influencers are the purveyors of the largest media. Michael Bey, Martin Scorsese, Woody Allen, Ridley Scott, James Cameron, Peter Jackson even non English speakers like Ang Lee.

I'm for the best, most accurate word for the audience. The problem for the English is that the language is not exclusively theirs any more and because they did not do what the French did, they have lost all control.