Anime includes a lot of wuxia-like stuff, but it's quite a bit more and the d&d monk is a super limited subset of the kinda stuff you regularly see in them.As much as I like some anime, this gets back into the debate about what a PC is: grounded in reality but with really cool stuff (Jackie Chan, Jet Li, etc.) or mystical, magical, and such (like anime often is).
I don't want to play anime style monks, etc. otherwise I would have stuck with the Street Fighter RPG back in the day. I'm totally onboard with that as a subclass that does that, but the core class should focus more on the broader idea of monk IMO.
Here's a couple good bits of history. That sort of anime is often representing the tropes of wuxia, but it can do it in a way that doesn't require blockbuster AAA movie budgts because drawing 20 some minutes of it generally costs the same regardless of the special effects type stuff they add to the wirefu.
14th centry seems close enough to king Arthur's 6th century