It’s his celebrity, it’s his money — so many of his positions are so antithetical to the interests of the donor class in the Republican Party that only someone with his own money and visibility could have done that. And, as you said, his shamelessness: He doesn’t care what people think of him.
That’s rare, particularly among rich, famous people. Most rich and famous people care very much about their image. And he doesn’t, and that’s a remarkable quality.But he does care...a lot. He carries grudges against people who say that he is a bad businessman or that he cheats (taxes, contractors, whatever) or that he is only where he is because of a rich father...or that he has short fingers.
There have been plenty of stories (I doubt this was the first, but maybe) saying the reason he got into the race in the first place was because Obama slighted him at the White House Correspondents' Dinner (I don't know if a better argument that that event shouldn't exist could be made). His entire net worth is a judgement on what the value of the "Trump" brand is.
He cares. He's just way too stupid to understand what he should do to actually get the respect he craves.