Eventually some meaningful competition from the likes of Don Bluth started to push them in the right direction (Secret of NIMH, Land before Time, All Dogs Go to Heaven, etc.) and not too long afterward they were doing things like Little Mermaid, Beauty and the Beast, Aladdin. Quite an improvement, though I dare say the storylines have never quite caught up. (Of course, all of Bluth's stuff would later be undermined as it was sequel-ized to Hell and back, like The Land Before Time XXIV: Teach Your Kids Roman Numerals Edition...)
Right now, though, after seeing Pixar's homages to Ghibli, I'm anticipating the impact of recent works like Puella Magi Madoka Magica, which really pushed some boundaries in Japan. (If you're not familiar with it, I'll just say... imagine if Pan's Labyrinth had been actively marketed to little children as a happy family film and an homage to Alice in Wonderland... and then translate that willful deception and the profound darkness onto Sailor Moon.) If it does make a splash in the youth entertainment industry at large, that will be quite interesting indeed.