In a community that recognizes Jewish law (there are currently none in the world except perhaps a few Muslim countries with few Jews in them), the man would be responsible for his wife’s spending until he gave the “get”, which is probably why this problem only arose recently (in modern terms, until he gives the “get”, she keeps the credit card, he keeps the bills). We should be arguing that the marriage contract includes the condition that the man will pay for the woman’s support until a “get” is given – which poses fewer problems than in arguing that the marriage contract is an agreement to arbitrate, since most state object to anyone submitting a divorce to binding arbitration (i.e. a contract to submit a divorce proceeding to a Beis Din is void as against public policy, unlike strictly monetary disputes).
The overall most effective solution would be a takanah that no one can go to a civil court to ask for a divorce or separation until they have given (and accepted) the “get”, and (THIS WOULD BE RADICAL) if one side doesn’t cooperate then the Jewish community would pay all the legal fees for the other side (probably through a public interest law firm). Faced with having to fight someone with deep pockets (i.e. the frum public interest law firm, relying on tax deductible contributions and pro bono lawyers to supplement paid staff), most people would avoid litigation.
It should be noted that whenever anyone loks for statistics, most so-called “agunahs” resolve themselves in a short period of time, suggesting that most get-refusal involves men who hope to “save the marriage”, which is normal but is also a self-limiting problem (they give up after a while).