I would be very surprised if the rule, in some states, of being apart for a year to finalize a divorce, has anything to do with religion/church. Most likely, it is a relic of legislation attempting to define "litmus tests" on which the judiciary can make decisions.
Keep in mind that with things like divorce and child custody/support, couples change their minds (sometimes a lot). Our court systems can't handle this (certainly not the costs). Over the years, our societies have required legislatures to define rules and processes for lumping everyone into a process. I don't think the state really wants to be involved in divorce cases, but there are reasons they are (property, debts, retirement benefits, child custody/support, etc).
Like it or not, state courts have to be involved in divorces. For some couples that can handle it without the courts, well, like education, they get dragged down into the mean.