I used to be all in favour of state churches (like each of the Scandinavian countries have, and UK, to an extent).
Mainly because it's just a nationalistic thing and because they look after the actual churches; many of which are fantastic historical / art treasures. If the didn't, the churches would start to decline.

However I changed my mind after hearing some Americans describe the USA's strong views on separating church and state, and why they came to that conclusion. I thought their views were sounder at the end of the day, and stood up on their own merits. Mine were based on subjective feelings and hopes.

Plus, the faith of state churches quickly become either opressive, prescriptive and stifled, like happened a few hundred years ago.
Or they become populistic, trying to please everybody and sacrificing their own dogma, like today, when their policies are nothing but state policies, cloaked in supposed Christianity.

Plus, state churches only work when >99% have the same religions, and that's just not the case anywhere anymore.