The Ramban writes (in the introduction to his sefer Milchamos Hashem) that the study of Talmud is not like mathematics. In Talmud study, a halachic analysis is not a geometric proof and its validity need not be contingent upon accurate application of hard logic to unassailable axioms; nor is a halachic analysis deemed invalid only upon demonstration of incontrovertible logical errors or fallacious assumptions. What is significant in halacha is the approval or disapproval of halachic experts, implying the reasonableness or unreasonableness of the argument. One must have a strong tradition in psak halacha (rendering of legal decisions) or one can float so far off as to develop the most ridiculous ideas, all in the name of halacha.
The Torah prescribes the divorce procedure such that the husband must participate voluntarily. When he refuses to participate, his wife has no other means to be free of her husband, and while she remains legally married to him she may not marry another man. This situation, though unfair and tragic for the wife, is essentially the creation of a man who has shown himself to be an evil criminal, and is abusing his wife in this contemptible way. He has made her a virtual agunah as the husband alone has the authority to free her. Over the many years of our history the rabbis have done whatever they could for any woman so trapped in this lamentable predicament. Unfortunately, no categorical or general solution to the problem emerged.
About forty years ago an Orthodox individual proposed a solution. He reasoned that the woman requires a divorce only if she is married. Although annulment is not an option, it may be possible to find cause to invalidate her marriage by finding a fatal flaw in her wedding. For example, the wedding requires that the groom give the bride an object of sufficient value, one that the groom is entitled to give, while declaring his intent to thereby marry her, without deceit in any of the particulars, all under the watchful eyes of legitimate witnesses. If any of these conditions are not met then the wedding is fatally flawed. Likewise, if the bride or groom deceives the other in a material way, the other may legitimately claim that the entire wedding was under false pretenses and thus void. Thinking along these lines, the individual referred to above argues that if the bride and groom had realized that their personalities were incompatible, they would never have agreed to get married. Hence, the marriage was effected in error, lacking the requisite da'as (awareness) for a wedding, and no Get is needed to separate them because they were never married. At the time, Rav Yosef Dov Soloveitchik declared this suggestion ridiculous. As the years went by, the ridiculous has become the sublime.
To appreciate why this suggestion is ridiculous, we must understand the institution of hataras nedarim (annulment of vows). The mishna at the end of the first perek of Chagiga records that this institution does not really appear in the Chumash (Five Books of Moses). It is known only through the oral law. The method used by the beis din (rabbinical court) to nullify a neder (vow) is by undermining the da'as (mindset, awareness, commitment) under which the vow was taken. The individual who took the neder points out his lack of knowledge (or, more commonly, lack of foresight) of some aspect of the neder, and explains to the beis din that if he had considered the possibility that events would show the neder to be improper, he would never have accepted the neder; whereupon the beis din declares the neder as lacking da'as, and therefore a neder ta'us, which is not binding.
This special method of invalidating a neder applies only to nedarim and such cases that belong to the category of hafla'a (e.g. - shavuos (oaths), hekdeishos (consecrating material goods to be the property of the beis ha'mikdosh), n'zirus (assuming the status of 'nazir'), the separating of teruma (tithes to kohanim) and challah). Thus, one who separated teruma and later regrets it may petition the beis din to reverse the act (naturally if other conditions are met). By contrast, one who regrets buying some shares in a corporation, or selling his house, for example, can not appear before a beis din and have the beis din annul the sale or the purchase based on the fact that he was unaware of all the consequences. Because mekach u'memkar (business transactions) require a higher level of da'as to create (than does hafla'a), a stronger, more obvious form of ta'us is needed to void that da'as. Consequently, one could not justify invalidating a business transaction on the grounds that it was conducted "in error" even if the error would qualify as such for a hafla'a (unless, of course, the error was sufficiently evident).
Furthermore, kiddushin (entering into a marriage) apparently requires a level of da'as even higher than mekach u'memkar (see the famous comment of the Ran to Nedarim 87a. See also Beis Yitzchak 5748, pg. 241). In order to nullify a marriage by reason of kiddushei ta'us (because of lack of da'as), one would presumably require an even more obvious ta'us than what might be sufficient to invalidate a purchase of stocks or a sale of real estate. Indeed, the Talmud (Kesubos 73b) describes certain cases that based on the general principles of ta'us would qualify as kiddushei ta'us and as such would be invalid and should not need a get. Nevertheless, the gemara declares that a get is required- either as a chumra d'rabanan (rabbinical stringency), or perhaps even because of a safek d'oraysa (legal doubt on the biblical level). It is plain from this source that we are more reluctant to invalidate a wedding on ta'us grounds than to declare a mekach taus on a business transaction.
To declare a marriage a kiddushei ta'us because the wife didn't realize that the husband would be unsuccessful in holding down a job and earning a living is simply unacceptable. To invalidate a kiddushin due to ta'us the halacha requires an extraordinary mum gadol (very significant defect), with a very obvious umdana d'muchach (compelling assumption) that no reasonable woman would agree to marry such a man (see Teshuvos Beis Halevi, vol. 3, pg. 23).
In our case of the obstinate husband, the proposed ta'us is on the part of the woman. Interestingly, the Beis Halevi (3:3) quotes poskim who were of the opinion that as difficult as it is to declare the da'as of the husband as taus, it is even more difficult to declare the da'as of the wife as such because the Talmud presumes that women are more interested in companionship than men, and therefore would agree to marry someone even if he has a mum gadol, unless he has an extremely unusual mum. The Beis Halevi himself disputes those poskim , however, arguing that this presumption is not relevant to the issue of declaring the mistaken consent of the bride a ta'us. Rather, both parties should be equal - declaring as ta'us either da'as of the bride or da'as of the groom. Nevertheless, no posek ever suggested that one could declare as ta'us the da'as of the bride in a fashion similar to heter nedarim.
Not only is it a mere impropriety on the part of any beis din to permit a woman to remarry based on such flimsy grounds; even bidieved- if a beis din granted a married woman permission to marry on these grounds- the ruling is ignored, and such a "heter nisuin" issued to the woman is meaningless. Only in the case of a neder do the rabbis have "power" to nullify a commitment by rendering it as a neder b'ta'us, even if it was not manifestly taken in error, as described above. However, in all other areas of halacha- particularly those of marriage and divorce- either the kiddushin falls apart by itself because there was a "mum gadol" and an umdenah demuchach that there was no da'as; or the marriage remains - notwithstanding what any rabbi or any beis din says. The special halachah of "hatarat nedarim" that empowers the beis din to undo a neder retroactively by proclaiming the da'as as a taus only applies in the area of "hafla'ah".
Moreover, even in the case of a sale that was canceled because of a mum, the Rambam wrote (Mechira 15:3) that if the purchaser continued to use the item after having discovered the mum, he cannot later claim mekach taus. Continued use of the item indicates that the level of the ta'us is insufficient to warrant voiding the transaction. Likewise, it is transmitted in the name of Hagaon Rav Moshe Feinstein zt"l, that even in the rare case of an unusual mum gadol, through which the wife would be able to remarry without a get because of the ta'us on her part at the time of the wedding, if the woman didn't walk away from the marriage immediately upon discovering the mum, the halacha of ta'us cannot be applied.
Rabbi Eliyahu Ben Chaim (Yeshivas Rabbeinu Yitzchak Elchanan) published an essay in the Yeshiva publication, Beis Yitzchak (5758), explaining the mistakes of these "batei din", and cautioning the agunot not to rely on such meaningless "heterim". In his essay he quotes Chacham Ovadia Yosef as having said the same.
It certainly is a great mitzva to help an aguna escape her plight, but issuing a heter nissuin (permission to get married) to a woman along the lines of heter nedarim is simply a farce. Let us not make a joke out of the Halacha.