The keyword here is "tried". Pretty much every other multilateral trade agreement is entirely undemocratic. Parties to the agreement negotiate on a condition of unanimity. This isn't just minority rule (Council/Commission), it's minority-of-the-minority rule.

The solution to the EU being "undemocratic" is to make it democratic: move decision-making power to the European Parliament and away from member states. You can have democracy or soverignity but not both.