That’s interesting. Is this phrasing used by others or is it your own? I haven’t ever heard it before. As an anime/manga fan, it seems confusing and slightly grating. It feels similar to intentionally wrong or “not even wrong” engagement bait.
The closest thing I can think of that I myself could describe that way would be Alita: Battle Angel, due to the big eyes/small mouth style of Alita, but I would never actually call it live action anime, but rather, a live action anime adaptation.
Maybe this is related to modern speech patterns? The closest thing I can think of is “it’s giving x” which seems to me to be a shortened version of related phrase “it’s giving x vibes.”
On a related note, The Matrix actually has an animated spinoff The Animatrix, which has segments that are arguably anime, as they are produced by Japanese creators in a typical style.
However, I find that the phrase live-action anime perhaps says more about the person saying it and their perspective than it says about the content being described as such.
I have never thought of its origins before, but I'd assume it's a short hand for "live-action anime adaptation". Maybe this makes it more palatable for you?
As for Animatrix, yes -- it really went full circle, considering how they pitched the original feature:
> When Larry and Andy Wachowski were pitching The Matrix to their producers, they played them a DVD of an 82-minute Japanese cartoon and said: "We wanna do that for real."
I think it’s mostly me. In another comment you mentioned the live—action Netflix One Piece adaptation as live action anime, and I think that description actually felt somewhat apropos in that specific case, due to the adaptation employing lots of CGI and special effects to ape the style and mannerisms of the anime.
I think finding the term live action anime slightly off is my own issue, as I also find the term Japanimation also slightly grating. It probably has something to do with being a fan of a historically somewhat mocked/maligned subculture.
Live action adaptions of anime and manga aren't even particularly new. There were plenty in Japan in the '90s (including pornographic ones). The earliest non-japanese adaption I'm familiar with was 2001's Meteor Garden in Taiwan, but I'd be surprised if it were the first.
The term is not well-defined.
You could say it applies to Ghost in the Shell, because it is based on existing IP of the genre.
You could stretch it to include The Matrix, which is an original IP but employs a lot of the style
Edge of Tomorrow, even though based on a Japanese light novel, has deviated enough both in plot and style for the term not to apply