The EU has done more to spread freedom and democracy than any other organisation on Earth. It projects soft power with a single carrot, the offer of membership.
The first success was rehabilitating Germany after the War. Spain, Portugal and Greece all used to be military dictatorships. Now happy, prosperous, modern democratic states. Admittedly there's been some unrest recently in Greece, but there is zero possibility of another military coup, it will stay free and democratic no matter what. That's because of the larger structure it belongs to.
Then it rehabilitated central and eastern Europe. All the countries that were offered membership are free and democratic. Every one of them. Doesn't that strike you as odd? All the non-EU candidates (Ukraine, Russia) are not. Coincidence?
Turkey is far nicer place than it used be. The army stays out of politcs. The Kurds and other minorities are being treated reasonably. All thanks to EU negotiators banging on about human rights during 30 years of talks.
What other organisation can boast such an effective record at democratisation?