The Rashba himself of course brings the passage about one who betroths against her will, and distinguishes it by saying that there the very act of marriage was done improperly. I am really uncertain about the exact point you raised: whether what the Rashba requires—”some trace of a get”—is indispensable or not. There are two possible reasons to say that it is indispensable: 1. One cannot annul (meaning, annul a marriage that was validly contracted, not the case of one who betroths against her will) a marriage. In all the Talmudic passages there is not really annulment at all; rather, the possibility of annulment causes the person to fulfill his condition. In the passages in Ketubot (3a) and Gittin (33a), the Rashba writes this mechanism explicitly, and so does Nachmanides in Ketubot. And one can explain along these lines the second passage in Gittin 73a as well (regarding a deathly ill person). 2. Really, the get is needed only for what you called “appearance,” but that concern for appearance was so important in the eyes of the Sages that they instituted the mechanism of annulment (again, when the act of marriage was done properly) only where there would not be a problem of appearance. Shochetman understood it like the first possibility [I think that is incorrect for some side reason, and I don’t want to go on too long].

On the other hand, one could say that their requirement of some trace of a get applies only where that is possible, as an added safeguard.
Is it clear to you that the second side is correct?

Three brief comments regarding the rest of what you answered:
1. Regarding precedents for using annulment after the period of the Talmudic sages, we found several precedents for this, but the overwhelming majority of them (except for one) were in a case of annulling a marriage that was contracted improperly (what you called “annulment from the outset”), and if so there is room to argue (and this is what Rabbi Gershon Rosenberg-Nissenbaum and Shochetman argue) that only annulment from the outset can be done after the Talmudic sages, but retroactive annulment cannot be done. Still, one could argue that the reason we do not find precedents is not because it was impossible, but because post-Talmudic sages did not want to do retroactive annulment without some trace of a get, because of the heavy price of appearances.

If we hold that making the money ownerless/confiscated would be effective to annul a marriage, then yes. But it is not at all simple that confiscating the money annuls the marriage; the marriage has already taken effect, and straightforwardly confiscating the money would not annul the marriage, just as you yourself wrote.
It seems to me that an average person conditions his marriage on the Chief Rabbinate as representing religion, but you think (like Atlas) that this is a condition imposed by the Torah and not by the person. I will only note that from the wording of some medieval authorities (the Ra’ah, Ritva, and others) it seems that it is a condition of the man betrothing himself. But that is already a separate discussion.
Thank you very much!

I didn’t understand. A person who sent an agent to deliver a get and then canceled it not in his presence—what condition was fulfilled here? Possibility 1 is really very puzzling and unclear. How can one say that annulment is ineffective without a get, unless you invent that the Sages enacted a rabbinic ordinance not to annul without a get. But that brings us back to the appearance approach.
1. I do not understand how one can distinguish between different annulments. If we have the ability to do as the Talmudic sages did (that is, that we do not need the greatest religious court of the generation), then we can do everything, and if not—then we can do nothing. Unless we are talking about the mechanism of confiscating the money, as above.
2. Confiscating the money annuls the marriage retroactively. True, it is strange and surprising, but it is explicit in the Talmud: “Granted, if he betrothed with money…”
3. Indeed, I know that there are medieval authorities from whom it appears that this is a stipulation of the person, but that is clearly unreasonable. They already went at length in raising difficulties with that (for example, that a person who acted improperly does not condition his marriage on the sages).

I am copying the Rashba’s wording in the passage in Gittin: “The rabbis annulled his marriage—that is, if he were to cancel it, the Sages would annul the marriage, and because of this we are witnesses that he does not cancel it in his heart, so that his intercourse should not be promiscuous intercourse.”
And I didn’t understand—why is it not understandable that the Sages required a get / one witness to death, in order to be able to carry out annulment? If they thought that without a get there would be a problem of appearance, then they determined that the annulment would be only in a case where there is a get. Does that seem far-fetched to you?

Regarding the numbered comments:
1. I agree with you. But to explain the logic of Rabbi Gershon Rosenberg-Nissenbaum: annulment from the outset is easier because it prevents something new from beginning. It is easier not to apply something new than to stop something already existing.
2. Presumably the Rabbi knows that there are many interpretations among the medieval authorities, according to most of which the phrase “Granted, with money” is not because of the principle that property declared ownerless by a religious court is ownerless, but for other reasons. [Money marriage is rabbinic, or with money the Sages have no problem annulling because there will be no negative result, unlike intercourse, where the result will be promiscuous intercourse.]
3. The medieval authorities who explained it that way explained it regarding the passage in Ketubot, where the marriage was done properly. In cases where it was done improperly, it is obvious that this is not a matter of the man conditioning it on the sages, and there they would have to say that the Sages uproot it through positive action. [Tosafot already discusses this in Bava Batra.]

By the way, according to your view that marriage can be annulled by confiscating the money, then it is obvious that one can (without getting into the question whether it is advisable) annul today any marriage at all (for today all marriages are done with money) for any purpose? [get-refusers, mamzerim, a woman whose husband is in a coma, and the like]

I didn’t write that it is far-fetched. I said that straightforwardly, if annulment is not limited only to the cases established in the Talmud, there is no good reason to think that they determined a priori that there are no annulments without a get. Beyond that, even if they did determine this, that is at most a rabbinic prohibition, but the annulment itself straightforwardly still exists. And one can discuss, in difficult cases, violating that rule and annulling anyway.

1. Whether it is easier or harder does not matter. My claim is that in principle one should not distinguish between annulments. If this is possible, then that is possible too, and vice versa.
2. The simple and prevalent interpretation among the medieval authorities is that this is by virtue of the principle that property declared ownerless by a religious court is ownerless. The fact that there are other esoteric interpretations does not matter for our purposes. Beyond that, even if there are other interpretations, some of them were said only according to the conclusion of the Talmud when they expanded beyond marriage by money. But in the Talmud’s initial assumption it is even clearer that this is the intent.
3. If they have the principled ability to do this, that is what matters. I do not care that in certain cases there was no need for it. The discussion is whether it is possible in principle.

As for your last comment: absolutely. That is precisely the difference between a situation in which there is a central government (a king) that has authority to confiscate money, and authority that the Sages took for themselves to confiscate money that they do not actually control. The question whether it is appropriate to do this is, of course, a different question.