Folks had to go into court to PROVE a wrong by the other party.
Giant "he said, she said" fest. Enormously expensive.
But it was not one sided. If a man could prove infidelity, drunkenness, neglect...he could avoid alimony and gain custody of the kids.
Not so today (which you are probably aware of). Even if the husband can absorb the enormous legal bills of going through "divorce court", fault divorces are hardly issued anymore. No-fault is easier for the state and usually ends up leaving the aggrieved spouse destitute with debt for a number of years.
Correct and that's the aspect of this they are desperate to avoid.
Single women with children are for all practical purposes married to the state and seek to maintain a stable relationship with the State above all other relationships, even above the relationship with their own children.
"After all", they reason, "I have to make concessions to the State in order to be a good mother to my children".
So, they ignore abuse of their self and their children in the government schools and social "safety net" system that's usually far more demeaning and psychologically abusive than anything their former husband was guilty of.
In any case, AFAIK divorce is still expensive. Just because the divorce itself is a moot issue once one party files, there's still all the squabbling over assets and custody.