Getting off-topic but an issue with these state churches is that they usually get become super liberalized with progressive theology. They don't even manage to pass on this progressive form of Christianity; rather the trend in countries with these sort of state churches is the population ends up becoming super secularized even if they still remain nominal state Christians via paying taxes and having weddings/funerals in their state churches.
Look at countries like England, Finland, Denmark and the like for the prime examples. These countries are some of the most atheist ones with large amounts of people being actively hostile towards Christianity despite them having flags with Christian crosses, required religious education, and laws on the books that promotes Christianity. US, on the other hand has a Constitution that prevents all of these from happening yet the nation has consistently been more religious then western Europe throughout it's entire history. Tocqueville when he was touring the US in the 19th century already noticed how much more Americans were devoted to Christianity compared to Europeans.
Look at countries like England, Finland, Denmark and the like for the prime examples. These countries are some of the most atheist ones with large amounts of people being actively hostile towards Christianity despite them having flags with Christian crosses, required religious education, and laws on the books that promotes Christianity. US, on the other hand has a Constitution that prevents all of these from happening yet the nation has consistently been more religious then western Europe throughout it's entire history. Tocqueville when he was touring the US in the 19th century already noticed how much more Americans were devoted to Christianity compared to Europeans.