Well, personally, I can't help but feel it's due to a tendency that developed in which western aesthetics and imagery became more desirable for the Japanese. You can say that "all cartoons have big eyes" and so on, but most other cartoons you will be referencing are of western origin, and yet still don't usually place such heavy exaggerated emphasis on typically western aesthetics as anime does. I believe that if you look at years gone by, small eyes and aesthetic features that were typically very Japanese were what was highly appreciated in Japanese society (and it seems to make a lot more sense to value your native features), so this suggests that it wasn't always a case of "wanting what the 'others' have".
I have suggested this in the past and I know some disagree, but I think the western influence and almost 'imperialisation' of beauty over the rest of world, is having devastating consequences for many people's perception of their native appearance. The amount of cosmetic eye surgery's that take place in countries Japan, or the bleaching of skin in places like India, or the Caribbean islands appreciation for "lighties" supports this argument. If you go to many of these countries and you watch the TV or look at magazine covers your almost guaranteed to see an overwhelmingly disproportionate number of models or actors who all have western features about them. That's what people are consistently being told is 'attractive'.
I think it's shame, and I think the situation should be addressed so that there is more balance.