Japan should absolutely be proud of their amazing gaming legacy. There is an unexplainable style and flare to Japanese action games, and non-Japanese 3rd person action games come across as jank to me fairly often. I'm sure there are exceptions to this, just not as many.
The term that's stuck for this subgenre (for better or worse) is "Character Action". It's not particularly descriptive - I agree with Kamiya in that it ought to make clear that it's in reference to the Japanese school of action game design, which is very distinct from western sensibilities.
That said, I'd consider the best western take on the genre is the indie game Furi.