What can be done about the problem of bullying in post-PhD academia?
I'm not sure that I accept your premise that "academia is paradise for bullies". There are bullies in academia, but also there are bullies elsewhere. 

Nevertheless, we can meaningfully ask if there are any dynamics in academia which may help bullies prosper. I can think of two particular ones:


Some parts of academia have a culture of tolerating and in some cases venerating "the brilliant asshole", i.e. the arrogant academic who routinely belittles and harangues students and junior researchers but we all go along because they've done some really important work in their field. Your question hints at this and user104075's answer kind of exemplifies it. This attitude can lead people who should really be seeking to prevent bullying to shrug it off with a "but that's just who he is".
Strong disparity in job security between the people at the top and bottom of the ladder, perhaps more so than in other professions. Postdocs are constantly, painfully, aware, that their contract will be up soon, and you need to get some papers, and there are hundreds of applicants to every faculty position etc etc. This makes junior researchers wary of leaving a position, even if it is terrible, and extra nervous of not getting a good recommendation letter from their present supervisor. I have heard of academics boasting of keeping their postdocs on short contracts, so that they can use the threat of not renewing it to get their postdocs to work unreasonable hours.
On the other hand, in some places, a tenured professor is virtually unfireable, short of outright academic fraud or serious criminality. So while the person on the end of the bullying faces huge risks from making a fuss, the bully may not face much consequence even if it does come out.


What can be done to mitigate these?


Use the wellbeing of an academic's students and postdocs as a criterion on which to evaluate them for funding and tenure
Better job security for postdocs - i.e. work towards a norm of longer contracts where possible. If this means that there are fewer postdocs, but they work under better conditions, I think that would be reasonable. Others will disagree.
Universities can implement robust anti-bullying policies with meaningful sanctions against academics who violate them.