Personally, I think the reason why many adults enjoy Miyazaki's movies is because despite teh seemingly shallow plot, there is a LOT to be said - people who say that shows with no plot inevitably suck are obviously very shallow because they haven't encountered a genre of literature and film which focuses on acute observations about life and details that would normally be ignored in stories with tons and tons of distracting plot. Not that plot is a bad thing, but no plot doesn't mean bad show...

For example, many adults (including Akira Kurosawa, iirc) enjoy Tonari no Totoro because of how accurately and effectively it portrays what it intends to (the beauty of the countryside, a simple life, the innocence of children, the charm of old fairy-tales that will only be around in your childhood, etc.) and evokes many feelings and emotions.

Normally, this sort of thing appeals to people who have had enough life experience to be able to empathize and appreciate subtle implications and portrayals of various aspects of life.