Those are primarily figureheads with limited power. The EU is not a presidential system. Which is good, because a single person can never well-represent an entire population, directly elected or not.

The council is more problematic, since a blocking majority might only represent 25% of the population (half of the EU member governments, each elected by majority vote), but in this case they voted in favor, so it's as if they didn't exist and the decision lies with parliament, whose composition is determined by proportional representation. Excellent!

The interesting thing here is that the EU is accused of being undemocratic not because special interests killed a law with wide support among the populace, but because all the different bodies might actually agree and pass a law that privacy activists don't like. Legislation by agreement of multiple cross-cutting majorities must clearly be undemocratic!