Ultimately, you ask "why can't D&D cater to my tropes?" And I my first answer was "because it does not occur to the current guardians of D&D that those tropes need special rules." The current guardians of "that which is D&D" either don't believe guns belong in D&D or (as I've conjectured) feel it is so easy to reskin bows as guns that it isn't worth printing anything about guns. Someday members of your generation of fantasy enthusiasts will take the reigns of "that which is D&D" and perhaps they will print such rules because, like you, they felt it would help a large enough segment of gamers to have such rules spelled out.
Have I made sense yet?
IMO, the idea of "the guardians of D&D" deciding what the game looks like is one of those things that isn't compatible with D&D in the next 10 or so years. WotC could sell every table exactly what they need. They just couldn't do it as a line of published books.
Things like the understated mouth and overstated eyes, the exaggerated "laugh" that looks like a Muppet with its mouth open, movements that occur without an animated transition, and speed lines without a background are key hallmarks.
It's interesting. The former two are very much animation universals. A lot of hay is made over, for instance, Bugs Bunny's "baby face": the proportions are all out of whack, because characters are cuter with bigger eyes and smaller mouths (except when laughing). Of course, the effect is more subtle on humans than it is on other things.
And the other stuff is definitely cultural difference. Japanese animation tends to be more accepting of the "surreal" elements (changing proportions), while American animation tends to ground itself. But you'll find wildly changing proportions in a good chunk of Canadian animation. Japanese anime is grounded in a very "cheap" style of animation without a lot of transitional cells and with cheap ways to depict motion that it keeps mostly out of convention and, well, because it's cheap, still in many shows. Reason being Japanese audiences kind of expect it, but American audiences don't have the same early animation experience with things like Astro Boy and Speed Racer, so they expect something different -- something a little more detailed, usually. But heck, check out the early 80's GI Joe and Transformers cartoons: full of cheap tricks that we might be totally used to, but that others would probably balk at.
There is a cultural difference in art style. But that difference is getting smaller. As far as D&D goes, none of those things are very applicable: art style isn't very relevant to what happens at the table.