I appreciate the sentiments offered here. I agree that once secular divorce has been granted, it is pointless to withhold a get and it is the high-road to give one.
However it really is similar to the partner analogy: one partner is a bum and refuses to honor his commitment. The other partner perhaps realizes that it is what it is and will agree to take the high-road and agree to dissolve the partnership. But he is hardly OBLIGATED!
So too here. A man or woman wishes to dissolve their partnership, causing harm to the other. The fact that they are resolute in doing the wrong thing and asking for an unjustified divorce does not entitle them in any way. On the contrary, it makes them more wrong.
What ought one to do? Sometimes it may be proper to hold the woman to her obligation and demand that she continue the marriage. One case that might be is when she will cause harm to their children as well. At other times the mentchliche thing would be to concede the battle, even if she is in the wrong.
All this applies to the man too, by the way.