I don't think I've seen a discussion on RWBY on here, so I'll just put "RWBY" here.
RWBY isn't anime.
Cool stuff.
One thing that annoys me about the Fate series is that they are really focused on non-japanese mythology. Which is cool because you get all the Alexanders and Arthurs and whatnot, but you'll never see an assassin Hattori Hanzo, or a Rider Takeda Shingen, or a Saber Miyamoto Musashi.
Call it a mild irking.
I actually like the heroes they picked out aren't Japanese. It's very refreshing to watch anime without it really being "about" Japan - Bleach, for example is "about" Japan. Attack on Titan isn't and that's one of the reasons I like it.
Also, it makes sense that (some) heroic spirits
wouldn't be Japanese. Out of the three examples you mentioned I've only heard of Miyamoto Musashi who I know to be an excellent swordsman, but people around the world are much more familiar with the great swordsman known as Arthur Pendragon than Miyamoto. Having Miyamoto be Saber instead of Arturia would've just been favouritism.
Gilgamesh as Archer doesn't make any sense since he wasn't known as an archer and actually isn't very well-known in any popular culture, but his sheer importance as being the hero-king of the most ancient city of the most ancient civilisation would pretty much force him into being a heroic spirit anyway, and the fact that he's actually well-suited to the position of Archer within Fate's world does end up with it all making sense (unless I'm confused about how heroic spirits are chosen to be part of the classes they're part of).