I think I've got it. Trump's appeal. He embodies, in a politician, the teenager-man that American loves in its movies. He IS The Teenager. Consider the types of things he says:
"America is a disgrace"
"I'm just saying what everyone thinks but won't say"
"Everyone is so biased"
"I'm really rich"
"I have a great car"
"You have a big problem"
Is he mature? Does he know policy or have solutions? Of course not--he's a teenager. He has emotion, bravado, immaturity, petulance. When other candidates or the media point out that he's not acting like an adult, he berates them for it. And the audience cheers. Because the audience doesn't want to grow up, either. They identify, thinking, "Why not let a teenager run the country? Might be fun."
A while back, there was an article by NYT Film Critic A.O. Scott that got a bunch of press, analyzing how American men in films and television had ceased to be about men who were adults or who were comfortable being adults and how this was mirrored in the culture. Perhaps he was already writing about the 2016 Presidential Campaign. What he wrote about our fictional characters seems to describe, well, the frontrunner of the GOP:
"We devolve from Lenny Bruce to Adam Sandler, from “Catch-22” to “The Hangover,” from “Goodbye, Columbus” to “The Forty-Year-Old Virgin.” But the antics of the comic man-boys were not merely repetitive; in their couch-bound humor we can detect the glimmers of something new, something that helped speed adulthood to its terminal crisis. Unlike the antiheroes of eras past, whose rebellion still accepted the fact of adulthood as its premise, the man-boys simply refused to grow up, and did so proudly."
We trend toward words like "egotistical" or "narcissistic" when we analyze Trump. But that doesn't explain his broad appeal, or the media and other candidate's inability to lay a glove on him. The proper word is "teenager."