The Kesubah is a pre-nup. In fact, in some states you can file a notarized kesubah in lieu of having a marriage ceremony. In court cases, some American courts hold that the kesubah requires that when the marriage ends, the parties agree to end it in accordance with halacha, as specified in the kesubah. The kesubah already requires the husband to give a get if the marriage ends, so if you make a secondary agreement contradicting the kesubah, it is inherently dubious. The secondary agreement (the secular pre-nup) implies the first agreement (the kesubah) is invalid.
And that’s before the complaints of many poskim, some of which have to do with whether an act taken pursuant to a civil court order is voluntary, and if under duress, is it then invalid.
My suggestion is to examine the historic reason why this wasn’t a problem, and I suspect you’ll find that the way it used to work was that if the husband wanted to ditch the wife, he would rush to give a get so he wouldn’t be getting the bills (since the wife could shop for anything she considered a necessity, and the husband would get the bills). Desiring to cut off paying the wife’s bills was not coercion, and would discourage refusal to give a get.