You really want to get the power of dividing things up, but if you end up doing a ton of work at the combination stage, you may not have gained anything.
By standing for a third, constitutionally dubious, term after a decade in power, and then staging a deeply flawed election, Alberto Fujimori succeeded only in dividing his country and antagonising the outside world, notably the United States.
With the Lisbon Treaty, those same national leaders have also ceded far more power than they realised to pan-European political parties, who imposed on them the deal dividing up the two posts, backed by the threat that nominees not to their liking would not be approved by the European Parliament in a vote early next year.