Maybe I understand now: if that woman didn’t care, then why does removing the covering incur a penalty?
It could be for the sake of educating the public in other cases. And perhaps that woman herself really was hurt, and the reason she did it herself was to earn the money. I think I addressed this question in the article about head covering according to Rabbi Mashash.

Yes, that’s what I meant.
The discussion in the article is about the prohibition involved [and the shame that results from it],
but in our case this woman has no shame at all. Even if she is embarrassed, the penalty can’t be worth more than the few coins for which she willingly agreed to remove the head covering.
In Bava Metzia the Talmud brings several views that “all Jews are princes’ sons”—Rabbi Ishmael and Rabbi Akiva, who say that a creditor does not collect an expensive garment even from a poor person who does not usually wear such clothes, and Rabbi Shimon, who says that it is permitted to smear rose oil because it is not evident that one is doing it for healing [since their way is to smear it even on weekdays], and maybe the strangest is Rabban Shimon ben Gamliel, who argues that luf is not set aside because we are all princes’ sons who raise ravens.

It looks like an argument between someone who shuts his eyes and claims some mystical quality of the Jewish soul, and someone who looks at reality and says: the facts show you’re wrong!

Not true. Of course she can be embarrassed. More than that, the embarrassment is not only worth the amount of a few coins: is there not a difference between her embarrassment before one person in his own room and removing her head covering before all of Israel as part of a process of humiliation? What’s unclear here?

“Before all of Israel”—where does the Rabbi get that from?!
And when she herself removed the head covering, after all, “he set up witnesses against her,” so she wasn’t alone, was she?

Even if he embarrassed her more than she embarrassed herself, that’s still a far cry from 400 zuz.

Even if you reject the proof from the fact that she embarrassed herself, it still seems absurd that an ordinary woman was embarrassed to the tune of 400 zuz. Also in the other disputes—for example what Rabbi Shimon says, that luf is not set aside because rich people have ravens and all Jews are rich—that is extremely strange.

We’re wasting our time.
First, you don’t know how much and before how many people she uncovered her head by herself. You don’t know whether the pressure of saving the oil caused her to do it. You don’t know before how many people that man uncovered her hair. And beyond all this, Rabbi Akiva says that she is allowed to injure herself but others are forbidden to do so. Meaning, even if from her standpoint it isn’t a problem, objectively there is major harm here, and she is allowed to harm herself.
Of course it’s also possible that this is an educational matter and not ordinary compensation as a matter of strict law (though that is not the straightforward meaning of the passage).

The connection to the other places that mention princes’ sons is not clear to me. Each case has to be judged on its own.

1. It doesn’t seem that the harm really was so significant if she agreed to it for a few coins, and the educational reasoning is possible, but it isn’t mentioned by any of the commentators.

2. If it’s impossible to ask from all the places, then I’m asking from Rabbi Shimon, which seems to me the hardest case.
[Rabbi Shimon permits moving luf on the Sabbath because it is food for ravens, and Jews do not set luf aside in their minds since Jews are princes’ sons and they want to feed their ravens luf. Does the Rabbi have an explanation?]

Abaye, in the Bava Metzia passage, brought a “list,” and as is known, a list (which is Abaye’s way) enumerates different laws (which usually are not accepted in practice). But there is no necessary connection between them. See the medieval authorities on the list in Sukkah 7b regarding a sukkah as a permanent or temporary dwelling. You’ll see there that there is not necessarily a connection between the laws. Here too this is about the laws of set-aside items, where it is enough that it is fit for ravens in order for it not to be set aside. And even the far-fetched reasoning that princes’ sons raise ravens is enough for that, so that it will not be set aside. There is no need at all to compare this with the other statements about princes’ sons.

Thank you very much.