Joseph, so maybe l’maaseh what happens in most cases is that the Beis Din convinces the husband to give his wife a get. Or as Lenny said, maybe once they get a civil divorce, that is grounds for a halachic divorce.
As I wrote to Lenny, I think that in general, men who refuse to give their wives a get are very much looked down on, and I think that most Rabbanim do consider personality conflicts to be a reason to get divorced and will try to convince the husband to get divorced.