Some interesting thoughts here.
I'm a fairly stereotypical INTJ (so basically the Devil, according to many). However, here's a weird fact: In my last job, in which I ran a department of between seven and ten people at various points over about twenty years, most of my charges were INFJs. For some reason, I just found them brilliant.
Also, I did not end up in that leadership position by choice. The last thing I ever wanted was to be a middle manager and I actively resisted promotion at several points - including one point where I pretty much demanded to be demoted. I got my wish after threatening to resign for a year or two, but then got promoted again. So yes, I think there is a certain inevitability to leadership.
The truth is that I hated corporate culture, and I'm very glad to be out of it. (I rant a little about it here, in point six, if you're curious/brave enough).