Cartoons are probably more respected as a medium for adults in the west than in Japan. There aren't really any anime with the mainstream recognition that something like The Simpsons had.
Mm, the thing is, I can't think of a single cartoon with that sort of respect that isn't a comedy. Or even one that's a sophisticated comedy (and not in the sense that Family Guy makes Futurama, older seasons of the Simpson, and ATHF look sophisticated). You don't have that sort of recognition very much with anime
yet, but the future prospects are much better than an endless stream of gag shows.
There's also the aspect of exposure; in the west, at least, given that (for example) the Simpsons started airing in what, '89? South Park started in the late '90s, and so on. You didn't see a lot of anime that wasn't purely children's material start airing in the West until around the turn of the millennium (with some exceptions and some quibbling about expectations re: content of childrens' shows in the west and east), and even then high-quality translations were rare things. On top of all that, it was something of a niche market that people weren't as prone to stumbling across as western comedies that aired on major networks.
Of course, that's all dealing with Western audiences, but I wouldn't be entirely surprised if the situation is much the same in Japan, albeit with the lack of gag comedy cartoons as a mainstream thing: your oldest main demographic is composed of 20-somethings who were about to enter or were going through secondary school while the first major wave of "serious" anime hit their stride. Expressing surprise that there isn't a large adult audience for anime is about as useful as doing the same in response to the fact that there wasn't a large adult audience for video games in the '90s.