Nitpick: Poland's President also has explicit executive roles. Probably Romania's, too. Russia's, Belarus's, Georgia's and Ukraine's, certainly.

People just don't understand the separation of powers

But those who set up a post should. A post is not all about the public perception. A Commission President answerable to the EP is enough. However, for a stronger sense of this accountability among the people, I think a change at the lower level is more important: an actual contest of ideas and for power between EP-parties, rather than consensus candidates of an eternal Grand Coalition. Otherwise, people won't get the sense that they can elect off a bad Face of Accountability even indirectly.

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