"Initially one would establish a court in another place and nullify [the get]. Rabban Gamliel the Elder decreed that one may not do so,
mipnei tikkun olam (Gittin 32a)."
As I noted in our introductory remarks to masechet Gittin it is, most appropriately, in masechet Gittin where we have recorded a series of rabbinic decrees promulgated in order to "fix the world". These were generally enacted due to man's inability, or shall we say unwillingness, to act in the best interests of others, something one is especially prone to as a marriage breaks down.
In most of the Talmudic cases discussing the delivery of a get it is an agent of the husband who delivers the get. When, and only when the agent actually delivers the get to the wife or to her agent, is the couple divorced. If the husband has a change of heart - perhaps the marriage can be saved after all - he may rescind his agency agreement effectively nullifying the get. However such could have disastrous consequences.
Jewish law allows one to rescind an agency agreement even without the knowledge of the agent. Thus in the case before us the agent could deliver a get without realizing that he no longer has the authority to do so. The wife thinking she is now divorced will remarry, thus engaging, even if unintentional, in adultery. Worse still any children born from this second marriage would be mamzerim, unable to marry most other Jews.
Alternatively the wife may actually hear of the husband's change of heart and not remarry leaving her an agunah.
In order to prevent such Rabban Gamliel decreed that one could only nullify the get in the presence of the agent, thereby eliminating the fear of having an invalid get delivered and the potential for mamzerim and at the same time effectively eliminating the fear that a woman be left an agunah.
Yet what if someone ignored this ruling of Rabban Gamliel the Elder and nullified the get by privately gathering three people and canceling the agency agreement. "Bitlu, mevutal, if he nullified it, it is nullified, these are the words of Rebbe [Yehuda Hanassi] (Gittin 33a)." Our Rabbis can make all the decrees they deem necessary but they may not abrogate Biblical law. The Torah allows one to cancel an agency agreement at will and no rabbi can change that fact. While the husband would be in violation of communal norms and subject to communal penalties the get is nullified and is no longer. We can try but we can't always succeed at preventing agunot and mamzerim.
However Rabban Shimon ben Gamliel, the son of Rabban Gamliel the Elder, says that once Rabban Gamliel's decree was enacted, a private nullification is rendered unenforceable, and the get would remains valid, for if not "of what use is the power of the beit din (Gittin 33a)?" To allow one to disregard the rulings of the courts with legal impunity would make a mockery of our court system. In order to maintain the integrity of the courts we allow the ruling of the Rabbis to stand even if such may go against biblical law.
This is all very nice but the Gemara is perplexed wondering how can it be that a get which according to Torah law is no longer valid (as it has been nullified) can per the ruling of the rabbis be considered valid, allowing a woman to remarry.
To this the Gemara answers, no problem. "Whoever gets married does so according to the approval of the rabbis and the rabbis annulled their marriage." By invoking the phrase "behold you are betrothed to me according to the laws of Moshe and Israel" one implicitly agrees to be bound by rabbinic teachings. And if one violates such by improperly nullifying a get we are going to invalidate the wedding ab initio. Surely that is better than allowing a mamzer.
But again the Talmud questions such logic. I can understand such if the man betrothed his wife with money or its equivalent such as a ring as when it comes to monetary matters a Jewish court can declare money ownerless. It then turns out that the husband did not own the ring he gave his wife when they married and thus there was no marriage.
Such annulment can work well but presumably only before the couple actually marry. What can the rabbis do, asks the Gemara, if they have been living as husband and wife for years. How can one annul a marriage if there are children and grandchildren who are products of this union? Yet such a scenario does not faze the rabbis. "The Rabbis declared their intimacy to be acts of indecency". In other words we prefer to declare that husband and wife were living in sin than to allow a situation where a husband can ignore the rulings of our Sages and potentially create agunot and mamzerim.
 It is readily understood why one would prefer the more impersonal use of an agent to delivering the get in person.
 Interestingly Rav Yochanan who expresses this fear, makes mention only the fear of mamzerim, ignoring the adultery that occurs in the process. As the woman has done nothing wrong in receiving the get the Talmud only makes mention of the hardship that will come to the children, who as in all cases of mamzerut are blameless.
 While the husband could still nullify the get it was now much harder to do so. As to the fear, which is so common today, that out of spite the husband would withhold a get causing his wife to remain an agunah, such was unlikely. Either such awful tactics like withholding a get are a modern invention or even if not, the rabbinic courts of the rabbinic era had much greater power than the ones of today. As far as I know there are no Talmudic cases of ongoing recalcitrant husbands as the courts "would hit him until he said I want to [give a get]." The hitting would continue until he gave a get or died of his wounds. Harsh - but effective.
 As is the case in all rabbinic decrees there is much to learn not only from the legal decree but also about the historical circumstances that led to such. It was forty years before the destruction of the Temple, when Rabban Gamliel was the Nassi of the Sanhedrin, that the Sanhedrin exiled itself unable to deal with the rampant corruption and disregard for social norms. The question of the Talmud was sadly far from theoretical.
 What Rashi, who offers this explanation, does not discuss is what would happen if a man were to marry and leave out the expression "the laws of Israel", the phrase which binds one to marry in accordance with rabbinic law.
 Recall that in Talmudic times there was a period of up to one year between Kiddushin, betrothal and Nissuin, actual marriage. Presumably it was during this time that divorce was more common than after the marriage itself.