Does Islam have to be political?

It seems to me that there is no country with a muslim majority where Islam is not used for political reasons. All of them have at least a few laws forbidding sex before / out of marriage, alcohol, leaving Islam, or a muslim woman marrying a non muslim. Why is the state watching over this behaviour, and why is it not left to the people themselves to behave? It seems to me that forbidding something by fines or jail time leads to a lot of hypocrisy. Not only from the people, but from the rulers too, and even more so since they can use islam for their own material gain. Is there any part of the quran (or hadiths, but I would rather have a quran verse) that says the state has to do this?