I find it hard to believe that Jesus was just telling them to get their paperwork in order. He seems to be referring to the reason that they are separating from their wives, not technicalities in legal process.
My views on this have changed a bit, over the years. I agree, that hardness of hearts is being addressed as the cause behind most divorces. But I don't see requiring a bill, or certificate of divorce as a mere technicality. Jesus was affirming the righteous standard that YHWH set.
I see YHWH's allowance of divorce as perfect, and merciful. Woman was created to be a suitable helper for the man, and it is in the nature of many to want very much to please the husband. Some men are not happy with their wives. They really can do nothing right (find no favor in his eyes). For him to keep her, when his attitude says constantly that she is unsuitable, can only be pride, or selfishness, to my way of thinking. The law seems to instruct such men to give her a divorce, and a chance at finding a husband she can please (is suited for, as "help meet" means suitable helper)
For a woman to be bound with no recourse to such an ungrateful man, would be worse then Biblical slavery, as slaves could run away from their masters, and were NOT to be returned. If God didn't require slaves to stay in bad situations, I cannot believe He intended wives to be abused like "slaves with benifits" (if you all get my meaning).
If the law said that a properly divorced woman was free to remarry, God meant it, and as long as sin is a choice man can make, divorce might, in some cases, be a very satisfactory solution.
It may be too, as earlier posters, and this thread's title suggest, that men divorcing their wives unjustly were commiting adultery, by causing what was supposed to be their wife/household/family to become part of another man's house. It's interesting food for thought (and study).