When Cora first announced that Kike' was going to lead off, I was so against the idea that I posted something to the effect of disowning Cora as my manager. Statistically speaking, Kike' has no business being a leadoff hitter. FTR, like you, I would have left Verdugo in the leadoff spot.
That said, my belief has always been that the way a manager manages his players is far more important than any in game decisions. When I say that I trust Cora's judgment, it is because of his ability to relate to his players and get the most out of them. He knows best how to put them in a position to make them successful.
As Bell pointed out, batting order really doesn't make as big a difference as most people think it does. Because of that, it's probably more beneficial to bat players where they feel comfortable as opposed to batting them where they should statistically bat.
There will likely come a time when Kike' needs to be dropped down in the order.