I would say it depends on what you are trying to achieve, and at what cost you are willing to pay to achieve it.
There are those who are willing to keep things quiet and allow their spouse the time and spouse to see if they make the right choice. And if not, the lbs moves on.
And then there are those who have a need be right, even if it destroys the bridges back to the marriage.
No single way is better for all people or all situations. But I think there are a few things that we can deduce which is what dbmod is suggesting. Those things are....
Exposing and letting the truth be known as you suggest will at the minimum cause the wayward much shame. Since at the time of actively cheating they are already proving they are very detached from their spouse, and probably don't respect their spouse or the marriage, it is probably safe to deduce that the exposure would be the nail in the coffin more often than not.
Allowing some time to pass increases the chance that the person would have second thoughts, and if not then the marriage was over anyway. No extra harm done to the mother oOr the father of your children, and therefore no more harm done to the children.
This is just my opinion, and I think DB principles make sense and offer a good chance of a correction in the marriage.
Exposure does work in some instances. I think it depends on the character of the spouse in question and their social circle. In my case, a lot of ny wifes family and friends know what happened and don't seem to particularly mind so had I done the exposure myself, I would have probably looked like a whining fool.
Perhaps if your spouse is a prominent person in the community, or is overly religious etc. Then exposure to people of influence may bring good results.
But generally speaking i think exposure, if it worked, would result in a reconcilluation based on shame not second thoughts. And I would bet on a repeat offense down the line, only next time they will plan it better so as to look like there was an exit from the marriage FIRST then there was an OP.
Just my two cents
Me, H-34 now 38 W-32 now 35 T-13 now 18 years M-6 now 9 Daughter 3 years now 7 Bomb 11/27/12 - OM 1 year in house separation Reconciliation 12/2013. Healed now 2017