I am also sure the study will show Donald Trump, Rupert Murdoch and Mark Zuckerberg run orgs with highly competent managers. But it is not competence in my book.
While I'm not sure how well managed any of those firms are, I think you can distinguish someone's business acumen from their personal failings, and admire one while denouncing the other. We already do the same for composers like Wagner or writers like Roald Dahl.
Wagner and Dahl don't have as much influence on society as corporations do. So I don't really agree with that comparison.
My issue is mindless ambition/win at all costs/do whatever it takes produces "competence" too.
The more data that pours in, the more we will realizes that stuff needs to be filtered out from our definitions of competence. The costs are too great imho.