The interesting thing about the gotcha paradigm is that it applies to both parties, and the public claims to hate it but brutally punishes candidates who screw up. Trump has proven immune to it, but the people who are refusing to punish him (by changing their poll responses) could easily have done the same for other candidates. They just...didn't, choosing to accept the media narrative that candidates need to be stale and calculated and safe.
It's the perfect game for the media, because it creates this guarded environment where everyone has to pander to the media and the public is constantly watching news reports to see who destroyed themselves that week. Good for Trump for refusing to play it and getting away with it, but it would be nice if the public could realize that it doesn't take a bloviating jackass to be immune to this game. It just takes the voting public refusing to play along.
I kind of liken it to men trying to succeed in the bar/singles scene. Or Tinder/texting, whatever kids are using these days to get laid.
Girls are continually throwing out tests for you to pass in a similar manner to the media. They might say "your such a pig, i didnt think anyone still held such backward opinions, i could never..." In this context, if you play it straight and back down, your night isnt going anywhere with the girl. She (unconsciously) is trying to find out if you're a pussy, and you failed. Most guys learn this by the time they're about 20 in the dating context. Why is it so hard for politicians to internalize it? Perhaps it's a hard move to pull off when your entire life is scripted and focus-grouped.
That's a juvenile analogy, but I think something similar must be at play with trump. A bit of whining aside, he has strong natural alpha dog instincts, and I think this endears him to a lot of people.