Neelie Kroes I had to look up. It seems to me that has no real experience in diplomacy or foreign relations, other than her current position as Commissioner for Competition, in which her mandate is largely limited to business and commerce -- hardly the profile I'd want for this position, but I'm not European, so what do I know. As a side note, the Wiki entry says she's "a confidant of Ayaan Hirsi Ali," and persuaded her to join the VVD, which IMHO should be a huge mark against her.
(Just nitpicking: van Rompuy and Barroso did gave up their PM jobs. Though, for fairness, Barroso did so to flee a sinking ship...) *Lunatic*, n. One whose delusions are out of fashion.