“That’s a pretty big deal, as the courts can sometimes mandate one party agree to a civil divorce.”
I’m not sure what you’re trying to say. The first Get Law says if the husband doesn’t give a Get but files for a civil divorce, the civil divorce is denied (and he remains legally married to his first wife thus unable to civilly remarry) until he gives a Get.
If “the courts can sometimes mandate one party agree to a civil divorce”, so what? The husband might agree to (and even want) a civil divorce, but the first Get Law allows the wife to have him denied a civil divorce.
All the first Get Law does is allow the wife to stop the husband from getting a civil divorce that he wants. Nothing more and nothing less. (The second Get Law is a whole different parsha.)