The only time public shaming is allowed for any violation of such things is when a beis din that both have accepted upon themselves – without another beis din taking the other side – says rhat one party, either husband, wife, business associate, etc, is in breach of beis din.
In most of these cases, there is always another side. R. Daniel Eidensohn on his site clarifies this with proof in most of the high profile cases. In one neighborhood, placards with a man’s face and name were distributed on streets, while one beis din was apparently on his side. That is indefensible. Women sometimes wish to take away mens’ entire lives, both in terms of their children and their money. There needs to be a bargaining chip; the man can say that if you want to extort me and take money just because goyishe law says you’re entitled to it (even though she didn’t work for it at all, and even if she was working her wages go to her husband) then you won’t be able to remarry.
I don’t see what’s wrong with that scenario, bitter and sad as it may be. Are there cases where one party is clearly wrong? I’m sure there are, but mindlessly shouting how many years a woman has been an Agunah (and exactly how many are there? 50 in the nyc area?) does not mean she is right.
In almost all of these cases, if a woman would agree to not take any money besides her kesuvah(if she’s entitled to it…her wanting a divorce because she isn’t happy makes her lose that right, a taanah of “maus alai”, which is extremely common) and agrees to joint custody, I’m sure that 95% of the time this wouldn’t be an issue.