I could see why this rubs you the wrong way.

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."

https://www.theguardian.com/film/2009/oct/19/hollywood-ghost...