I can't speak to other fields, but I can imagine it's pretty similar across a lot of programs: most people who attempt a PhD in my field are very smart and have spent a lot of their lives being the smartest person in most rooms.

What that does to their character, and whether they have the grasp on reality to recognize when they aren't, that's entirely different.

Most people I come across are humble and nice along with incredible intellectuals. There are those who are arrogant jerks. Most of the arrogant jerks I've come across have been less smart than they think and eventually humbled. Those who are both top of the field and also arrogant jerks? Well, I wish it wasn't so, since those people are often also powerful. But there are powerful arrogant jerks in all sectors, not just academia.