[ajb]

Are you aware of the history of the US Senate? It had exactly the same problem. Senators were appointed by the political elite of each state.

But, once one or two states decided to elect their senator, it was game over. The other states gave up, and now all the senators are elected.

It's true that both the commission and (perhaps even more powerful) the council of ministers are not democratic. But this is in the hands of each individual country to change. And it's national level politicians who are currently the obstacle. All find it easier to blame the EU than to take responsibility for change. But if one country takes action to increase , even a small one, the public in the others will realise they all can.