I think that's a very bad idea. A permanent President of the European Council is already problematic for making the Council even more influential (we discussed this a lot already), even if the EP picks its head (national governments would have a much stronger incentive to exert influence on MEPs), but your idea would permanently undermine the separation of powers.

give the EU a real "face" of accountability and democracy

I think EP election of the entire commission counts more in that field than that of one single man. (I still don't like Presidential democracy :) )

_{*Lunatic*, n.
One whose delusions are out of fashion.}