Hello Rabbi,
Just a brief note: it seems that Ritva already preceded him in this… See Ritva on Sukkah 2a, in his commentary on the Mishnah, where he addresses the question raised by the medieval authorities as to why the Mishnah on 9a explained what an old sukkah is, when according to Beit Hillel an old sukkah is valid anyway. In one of his answers he explains that even according to their view there is a practical ramification, when a person forbade himself by vow from using an old sukkah.

Thank you very much. I would just note that there are several differences:
First, clarifying the position of Beit Shammai is itself something with practical ramifications. But that is indeed what Ritva answers in his earlier answers.
Second, here we are not dealing with the law of an old sukkah, but with the concept of an old sukkah. Ran’s practical ramification is from the law of the Sinai ox, but Ritva’s practical ramification is in the concept of an old sukkah.
And third, the dependence here is direct. Ritva’s practical ramification is in someone who vows concerning an old sukkah, and not in a woman’s betrothal or someone vowing Naziriteship on condition that an old sukkah is such-and-such.
In fact, a person can vow regarding an old sukkah, meaning to be stringent like Beit Shammai (assuming that here we do not say that commandments were not given for benefit, and that is not our topic here).
But still, the principle is somewhat similar.

To be honest, I never understood the answer, "a practical ramification for a woman’s betrothal," because—

If truly the only practical ramification is the betrothal, then it is not really a practical ramification, because whether the husband betroths on condition of this side or on condition of that side, they are exactly the same thing! It is the same content! Either way, the woman is betrothed!….

Therefore I always explain that "a practical ramification for a woman’s betrothal" means that there certainly is some practical ramification, only at the moment we have not found it.

That is how it seems to me.

I disagree. There can be situations in which the content is different and yet there is no practical ramification. For example, the prohibitions of neshekh and tarbit are two different ideas even though there is apparently no practical ramification between them. Your view is similar to what is called in philosophy logical positivism—that whatever has no empirical content has no content at all.

I meant something else.

Certainly, if there are different ideas, then that itself is the practical ramification—that is, a conceptual ramification and not a practical one in action (and that of course carries over into a practical ramification for a woman’s betrothal). What I understood the phrase "a practical ramification for a woman’s betrothal" to mean was that even though the content is completely identical, and only the wording is different, that is the practical ramification (for a woman’s betrothal). About that I wrote that in my opinion this is not correct. If the content is identical (and it is not merely that there is no practical ramification), then there also will not really be a practical ramification for a woman’s betrothal. It is the same thing.

It seems that you agree with this, no?

How could one not agree? Fine—if there is no conceptual ramification, then there is no difference in content. That is a trivial tautology.

So one can summarize that the content of the phrase "a practical ramification for a woman’s betrothal" is that there is a ramification in the content of the matter, such that although right now the two sides appear completely identical, in fact there is a difference in content (and therefore there is a practical ramification for a woman’s betrothal). But it was never meant to say that even when the content is identical there is still a practical ramification for a woman’s betrothal just because the language is different.