WRT the UK vs. US...er, comparison, you subjects of the Queen have an actual, bona fide established state church. Your (mostly symbolic) Head of State has, among her titles, "Defender of the Faith" (though I'm not sure how much defense she actually provides...).
Hmmm... Maybe we ought to try that, since it seems to have worked for you lot... "OK, Mr. American Patriarchy Association dude, we'll make the US a Christian Nationtm but first all you Christians have to get together and agree on exactly what doctrines the Church of the United States will preach and whose hierarchy will get to be in charge of it. We'll give it half of the Pentagon's budget." Then all the nutjobs massacre one another until only a handful are left, and the Ninth Circuit Court hands down a ruling that says, "Uh, guys, First Amendment?" We say "Oops!" and call the Church O' the U.S. thing off now that there's nobody left who wants it.
I do find it strange how people who despise every conceivable action of the Federal Government (besides blowing up dark-skinned people on the other side of the globe) are so desperate for its sanction on their religion, which they apparently want to turn into a (*gasp!*) government program. Conservatives, do you really want Socialized Christianity?!