There is and has always been a wide gap between the halacha in the sefarim and what happens in the real world. This occurs in most legal systems, especially in domestic relations matter. Most people getting divorced do not take out a Shulhan Arukh or a gemara to research the grounds – they have decided they can’t stand each other.
One or both of them want the other to be out of his/her life. One of them, usually the man, wishes to free of having to support the wife, and that can be exploited in getting him to give a get. It is very rare that someone is refusing to give a get, and also sending money to the wife since what he wants is for her to give him money (and if the man is cheerfully paying his wife’s expenses, it suggests the issue is that he wants a reconciliation and a rationale Beis Din will stall in the hope of it happening).
The various types of coercion (throwing him in jail, beating him up, etc.) are highly dubious since in all systems a legal act done under duress is invalid. Creating an economic incentive to give a get is no coercion – thus my suggestion that the Beis Din make sure the woman (in the typical case) has a free law who can enforce the support requirements and by representing the woman if the husband goes to civil courts, create a strong incentive for him to settle (fear of having to litigate against someone with deep pockets is NOT coercion by any standard, even if it has the same effect).