While you can read the republic as a political discussion, and I won't blame you if you do that given how piecemeal antique philosophers are often taught in contemporary academia, but in context it really is more of a discussion about the nature of justice, rather than a political manual. That is what he is trying to do, explore a just society would look like, and through it, trying to find the nature of justice. That is actually still a fairly interesting discussion.

Justice is very much part of the zeitgeist, but how many actually stop to ask what that even means? What does it mean for a society to be just, for a person to be just? If we can't produce an answer to those questions, how are we ever going to produce justice, or be just?

Plato's critique of democracy isn't something we should reject on the account that it's a critique of democracy. He makes a few good points, it's not some intellectual check mate, but it's something any follower of democracy should have answers to, they are problems any democracy needs to work toward solving. If there is any take-away from Plato, it is that we get closer to truth by asking questions, by exploring murky half-thought thoughts and figuring out where they don't quite add up.