Like “progressive”, “job creators”, “hard working families” and “pro-choice”, it is very hard to argue with something “natural”. Use other terms, though, (“left winger”, “capitalist”, “middle class” and “pro-abortion”) and you get something that plenty of people still agree with but others might have an issue with. Ditto with “natural” in English teaching book titles etc.
“Not natural” seems to usually mean “perfectly understandable, but not what a native English speaker would say” making “natural” something like “more like a British or American person”. That’s still relevant given the continuing influence of those countries’ arts, media etc on the language, but hardly the priority for the majority of our students who find understanding and being understood the main issue.