It votes on all laws so it has a strong power to stop bullshit. I fail to see how the amount of voters would remove that right. The power stands with the people who actually get out to vote.
Optimally, democracy is participative. People don’t just vote, they govern themselves. Alexis de Tocqueville’s “Democracy in America” does a great job capturing what that looks like. Today, the most democratic systems are what you have in the Scandinavian countries. Small, homogenous electorates can achieve social consensus on what their society should look like. And then they can act through parliament to effectuate changes.
The E.U.-wide electorate is so big and fractious that it has basically zero ability to achieve social consensus. And the E.U. Parliament has no power to initiate legislation anyway. So “democracy” is reduced to rubber stamping the initiatives of the Commission, which are in turn largely decided by the permanent bureaucracy.