It often depends on the state in which the parties reside, the decade in which they divorce, the particular lawyers they hire and/or the judge who hears their case. Divorce has no universal governing body. If there were standardized national divorce laws, they would be just as horrible as Obamacare or CommonCore. So it's often the luck of the draw. The divorce industry (lawyers, judges, therapists, accountants, etc) also have been crafting all kinds of ways to get around "no-fault" since its inception in the late 70s, and the results are not uniform by any means.
In SC that you mentioned as an example, it is still a "Bible belt" state where women may still invoke the hoop skirts-and-parasols stereotypes of helpless lil' wimmen. But in major cities of the northeast or west coast, there are lawyers who specialize in helping the stay-at-home spouses of professional men (lawyers, doctors, etc) who get absolutely destroyed by their husbands in divorcebecause they can. It's a patchwork all over the nation.
When our "free" society first started, there was a fairly uniform moral code rooted in Judeo-Christian values. "Fault" divorce actually penalized wrongdoings like adultery, abandonment or bigamy. "No-fault" was supposed to be an enlightened way for couples who agreed to divorce could speed up the process; but it soon morphed into a full-blown marxist assault on traditional morality, common sense and/or fair play. Now that four generations have had all that exploded in their faces, legal outcomes are anything some random judge thinks they should be whether he or she is having a good day or a bad one. It's chaos.
You are right to some degree (it varies by by state/local/judge), but according to NATIONAL statistics, women are 11x more likely to get child custody than the man is and 32x more likely to get alimony. No fault divorce simply screws men over, period. There are exceptions, of course, in a nation this large there always will be.