Democracy — meaning multi-party elections, checks and balances (executive, courts, legislature), freedom of speech, association and religion for everyone — is good. It is good because it protects unpopular minorities from harm, and ensures that an open discussion takes place about the country’s problems, rather than the closed group-think characteristic of dictatorships. For this reason, there has never been a famine in a democracy, though there have been plenty in dictatorships or colonial possessions.
Democracy has existed in the history of Yiddishkeit. In Jewish communities in Europe, for example, it was common for taxpayers to vote on how taxes should be levied and what they would be spent on. It is not alien.
Why do such regimes as the Taliban and Iran exist? In part, to show us that theocracy (even when partially or nominally combined with democracy, as in Iran) is inherently oppressive and dysfunctional, and prone to war and harmful nationalism.
If the charedim, in a few decades when they become a majority, try to set up an Iranian-style regime (in which a council of gedolim hold all the real power but elections still occur and have some influence, and in which vice squads roam around arresting people for holding hands or looking too Western), this will lead to disaster — civil war (the dati leumi would rather die than be ruled by charedi mullahs), mass emigration by the chilonim, economic collapse, etc. This is why we should value democracy, as a peaceful way of settling our differences and coming to deliberative solutions to our problems.
Even when Moshiach comes, who is to say there won’t be democracy (as in a constitutional monarchy, in which the monarch has certain powers and other powers are reserved for the legislature)? Even if Moshiach has ruach hakodesh and so on, he will not have unlimited time, and may not be able to decide personally on all aspects of how society should be run (what times should the local parks close, who should be the head dogcatcher of Tiberias, etc.)