@The Little I Know
The sequence you mention with the Rav and Beis Din may be the common way in the Hareidi community. I assure you they are not my clients.
BUT, many divorcing couples use Batei Din for a get who are not Hareidi.
Most area pulpit rabbis of all Jewish denominations (yes some here will object to the term) will not perform marriages of formerly married Jews unless there is a proper Get because the progeny could have mamzerus issues. The ‘reform’ grandchild of a 2nd time married Jew might become a BT and want to marry in the frum world.
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Again, the Batei Din I works with know the couple already has a civil divorce, has had counseling as required by CT law and are living apart. They are not involved in trying to save a marriage, but to dissolve it al pi halacha and make sure future children are legitimate.
In 35+ years I have taken more than 150 divorced Jewish couples through this process to obtain a kosher get.
Not one of these couples was frum, but some of their children and grandchildren are BTs.