I still think it's fair to say that the Commission does not represent the people. It is many steps removed from the people. Nobody voted for any of them.
According to wikipedia, this point of view makes me a euroskeptic. Which is not something I consider myself to be, I'm a big proponent of cooperation between European countries. But I am certainly very skeptical of unelected government officials deciding on far reaching legislation that infringes upon fundamental liberties. With zero political repurcussions or liability.
I can't really picture what a better structure would be. The elected member state governments should always be the ones driving policy. They need a way to get that done outside of their usual national structures and civil servants, so they create the Commission. People also want to feel represented in the final votes so we create the Parliament.
What would your structure look like?