This video explains why US adult animation is almost always comedic. US animation studios transferred their efforts to television in the years following Hollywood's anti-trust case (which meant future shorts were less likely to be assured of theatrical releases), but this was only cost-effective if the animation style was simplified and the content made child-friendly enough for extensive ad-heavy re-runs. With the exception of a 1972 series, adult TV animation waited until The Simpsons. Although this series was a risky investment, lessons learned from its rapid success allowed a transition from expecting adult animation to be unviable to expecting it to be viable as long as it was comedic, preferably in a sitcom format.
Clearly, adult anime is in a very different situation and has been for decades. (One need only look at the lists here.) The reason, in short, is that the historical factors mentioned above are unique details of US history. A similar overview of the history of Japanese animation, both cinematic and televisual, would sound completely different and make sense of the diverse range of adult anime that resulted, including in the present day.
So my question is: what are the key details of that history? (If it's an inappropriate question here, I might move it to History.SE instead.)
Edit for requested clarity: I'm referring to work with an adult target audience, without specific implications of sexual or violent content (though these could well apply in some cases).