It is quite common that the ultimate wrench in the mechanism gets used. It’s called “I want shalom bayis”. It forces the hands of the dayanim to “give it one more try”. A common excuse for a m’again is “I don’t want to divorce, I want to work on the marriage”. And because of the halachos of gett me’usah, the beis din is limited in what it can do. To be fair, there are as many women who refuse to take a gett, using similar excuses.
TLIK: Your characterization in this part of your comment is absolutely incorrect. Declaring a desire for Shalom Bayis, even if the other spouse is adamantly insisting on divorce, can and often is legitimate and sincerely desired.
Indeed the Torah, needless to say, is absolutely correct in extending this right to the husband; and Rabbeinu Gershom is correct in further extending this right to wives, where she previously hadn’t had the right Al Pi Torah, to insist on Shalom Bayis. Your opinion would indicate a belief on your part that Rabbeinu Gershom was mistaken in making the insistence of Shalom Bayis, despite the husband’s insistence on divorcing, a right for wives to veto their husband’s wish to divorce. Not to mention disagreement with the same Torah right husband’s have to veto a wife’s request for divorce.