I dunno. Look at The Catholic Church. No divorce per se, but they have "annulments." There are secular annulments, too, but they're generally not used very often. Anyway, whenever you set up a process for the church to analyze your marriage, you set up a system of potential abuse. Wealthy Catholics can get annulments so they can re-marry, which makes the ex-spouse angry, because the church is basically saying "Your marriage wasn't really a marriage. Good bye now."
I dunno...I think the church's role, ideally, would be pre-marital counseling and ongoing support during marriage, but...the local church doesn't have the same hold over people that it once did. Society has largley crumbled. Even without easy, breezy divorce laws, we'd still have a high divorce rate just because society is so hyper-indvidualistic, you know? "What's in it for me?" Not that divorce is always bad, but...
...OK. Like, my parents used to have marital problems. Bad, bad marital problems. But they were committed not only to each other, but also to the institution of marriage and, to some extent, to their notion of God and His rules. So, they stuck it out. They now have more resouraces than most people, which has improved their marriage, plus they've gotten older, so they've mellowed out and made peace with each other. There arne't many couples like that in the US anymore. Society says "follow your heart," etc. etc. If your marriage is bad, you go to counseling (because apparently "professionals" can fix your problems for $120 a session), and if that fails, you get another counselor for help w/ the divorce (because their magical words can heal your words, apparently).
Divorce isn't ever a good thing, but it does happen. We live in a Fallen World, after all. I think the church--to the extent that it can, in this age of social disintegration in the late, great United States--should offer guidance and compassion. But I don't think Protestants should set the church up with any major authority over marriage+divorce. I mean, look at what happened with the Catholics, lol.