Maybe it's the "Ooh it's from a foreign country and it's awesomely cute" mindset or whatever. I personally prefer cartoons over manga/anime, but I like anime/manga too(and my art style does admittedly derive a lot from it).
Its a little easier than some of your typical art styles. The big draw is the content, a lot of kids like various anime shows, and thus when showing their fandom they typically have an easier time with it than drawing, say, spongebob. (which for a square, I gotta tell you, is a very ambitious character to render)
As far as professional artists go, I find there is a constant melding of the two art styles, a east meets west deal. So why it may look anime at first, you'll commonly notice some western influences, and vice versa.
I dunno, really. I think it may be that the style is loose, allowing for more extreme expressions and movements without any pesky proportions. For instance, removing any given anime character's hair will reveal a huge ol' noggin, but it seems nice if you don't think about it too much.
Personally, I have a penchant for classic Western animation. I'm reeeaaal bad at it, but I appreciate the dedication it takes to get things just so. I am often disappointed these days to find that many movies are drawn in anime fashion when it doesn't lend itself to the medium (Halo Legends, Gotham Knight, Dante's Inferno); it's all because it's popular.
Anime and manga is made for a faster production, and that IS an industrial fact. Sailor moon pokemon and so on is CRAP from an artistic point of view. The proportions are fucked up, the general thing is that they are very looooong. Anatomy is often a town in russia, because.. well they obviously don't need it to be as accurate as a Renaissance painter wanted too. Plus it's all drawn fast, they don't have time to make it "right" .. in lack of a better word. Some times the eyes float around. As an upcomming animator i am really beginning to spot how poorly most animes is animated (and i'm sooo rookie), every artist can tell how poorly most are drawn.
Not saying some isn't good. There are some really pretty interesting stuff among all the crap. And i do watch some for the entertainment. Like FLCL, fucking hilarious
But it's only a product and it's selling well to the common man, he buys it. It's entertaining and foreign. Guess theres some form of fashion sense in it too. The way of telling the story might be more appealing to most, more exciting.