Some sins are generally recognized as crimes (think bestiality); others are nowhere regarded as crimes (coveting). By definition, if you want the magistrate to enforce the first table of the law according to the interpretation of the established church, you want to increase the number of sins that are regarded as crimes. That's not a condemnation of the view, merely a description.
What that highlights is that when people talk about "the establishment principle" they are not all talking about the same thing (or even necessarily clear in their own mind what they want). Established churches have historically ranged from maximalist (jailing and executing Baptists and conservative presbyterians; proposing the death penalty for sabbath breakers - see John Cotton's proposal for New England posted on one of these threads) to liberal (Scotland currently has an established Presbyterian church that refers to the WCF as a guide, but it has little impact on legislation). The question we keep asking is "What kind of establishment do you want?" For example, if the magistrate is to enforce the commandment about idolatry, he should be smashing stained glass windows and wrecking organs (as happened in Puritan England). But is singing accompanied by an organ a greater sin than refusing to baptize your child and advocating that others do likewise? And before you know it, you are jailing John Bunyan. I'm not sure how you have a maximalist establishment without going there (and requiring religious tests for many forms of employment - you don't want those pesky evangelical arminians teaching your children...). Immigration and citizenship is restricted to Reformed Presbyterians who believe in the establishment principle only. But if all you want is what is already in place in present day England or Scotland, I'm not sure it's worth fighting about. It confuses unbelievers, who think that being English = being CofE = being a Christian, but at least it leaves room for genuine churches to exist outside the establishment.
Then there is the utopian establishmentarian who is convinced that by the time we get the establishment, through the work of the Spirit, we'll all be sabbath keeping, psalm singing Presbyterians, so where's the problem? But if the eschaton needs to happen before we get an established church, it's hardly worth discussing in the present.