As a matter of fact, a woman's hair does not arouse sexuality in any unusual way — if you were a woman, would you wear a head covering?
Given what you wrote, there is no halakhic obligation here.

I didn't understand the question. I wrote that there is such a formal obligation.

What is a formal obligation? The reason for the prohibition no longer applies.
If you were a woman and you felt you looked ugly with a head covering, would you still wear one even though nowadays it has no reason behind it?

It isn't without reason. The reason is something other than what you think. Beyond that, the law must be observed even if in your opinion it has no reason.
It's clear that you don't have a basic understanding of Jewish law, so it's hard to discuss this or any other point of Jewish law. You need to study in order to understand.

You are plainly not coherent. Just for example: women do not go up to the Torah because of the dignity of the congregation; today that reason no longer applies, and therefore you have no problem with women going up to the Torah.
In short, wherever it suits you, you say the reason no longer applies and therefore things should change, and wherever it doesn't suit you, you say that even though the reason no longer applies we are still obligated to keep it because formally we are obligated.

He argued that from the outset a wig was not instituted because of modesty…

* That is, head covering

But because of what?

It's a bit hard to talk to walls (people who don't bother to read, or aren't capable of understanding). And it's even harder to talk to dogmatic walls. I'll write it again, and with this I'll end this bizarre discussion and retreat to my corner duly scolded.
1. A wig was not instituted. This is a Torah-level law.
2. In any case, the claim that this is a formal law means that it is not based on forbidden erotic thoughts. So it is incorrect to say that the reason no longer applies here, because that is not the reason.
3. By contrast, regarding women reading from the Torah, the Talmud explicitly says that it is because of the dignity of the congregation, and not a formal law.
If you want to continue the discussion and raise the same questions again, I suggest you copy this message of mine for yourself and save me from repeating the same points a third time. Thank you.

Thank you very much for the response, and I apologize; I did not mean to disrespect you.

The problem is not the respect given or not given to me. It interests me about as much as a garlic peel (and not out of humility, but perhaps the opposite, to my regret).
The problem is that people don't read what I write and then repeat the same questions again, questions that weren't especially strong to begin with. It's just trolling and needless bother. And when it's done with certainty and condescension, it's even more annoying, but that has nothing to do with any injury to my honor.
Forgiven.

It is hard for me to see a discussion of the wig issue that looks as though it was taken from the pages of the Talmud, just written in contemporary language.

You cannot answer a halakhic question, like one of the Tannaim or Amoraim, while completely ignoring the abundance of sources on this topic, from the Talmud down through the books of the medieval authorities (Rishonim) and later authorities (Acharonim).

I am not disputing the conclusion, but rather the strange method. Perhaps this is a general characteristic of all the responsa on the site — in any case, I am focusing on this specific responsum, and I will note my comments on it.

A.

1. In the Talmud in Ketubot 72, and Rashi there, we see that head covering is derived from something that is not explicitly mentioned in the Torah, but only incidentally; and Rashi explains that from the Torah we see that this was the custom of the daughters of Israel, a kind of “decree of Scripture” (what is called here a 'formal prohibition').

2. In the Talmud in Eruvin 100 it is explained where the custom originated, and not only among the Jewish people but also among the nations of the world (as explained by Rashi on Sanhedrin 58): the curse of Eve. This strengthens the argument that there is no element here of provoking erotic thoughts (what is called here 'problematic sexual thoughts').

3. In the Talmud in Berakhot 24 there is the law that “a woman's hair is nakedness,” meaning that it is forbidden to study Torah facing hair that causes erotic thoughts. The Talmud does not bring proof from the Torah law of covering the head, but goes further afield and derives it from a verse in Song of Songs, “Your hair is like a flock of goats.” Again we see from here that the Torah law is a decree of Scripture, a curse, and not an absolute determination that hair causes erotic thoughts.

4. The medieval authorities (Rishonim) there establish that the hair of unmarried women is not included in the law that “a woman's hair is nakedness,” and likewise the hair of married women that ordinarily comes out from under the covering. This determination again proves that hair is not “immodesty in itself” (or what is called here 'sexually arousing'), but only when it is ordinarily kept covered, in which case revealing it causes erotic thoughts.

From here comes the unequivocal conclusion that a wig, when it is a widespread custom among the Jewish people, among most Haredi women, has no element whatsoever that causes erotic thoughts, and is not “immodesty.”

B.

The answer is not related at all to the question. A “top-lace” wig (or any kind of lace wig) is a wig that blurs the difference between natural hair and a wig even more, by simulating the hair's growth from the head. Therefore this is an entirely different issue: misleading appearance. Do we forbid it because an onlooker will think that the woman wearing the wig is going with uncovered hair, or not.

On this issue, hundreds of halakhic decisors who permit wigs wrote that there is no concern for misleading appearance here, because the onlooker assumes that this woman (if he even knows that she is married) is wearing a wig and not going with her head uncovered, since the permission of wigs is common and routine.

The onlooker does not have to 'know' that the woman is wearing a wig; it is enough that he imagines that it is a wig.

So too, for example, the halakhic decisors wrote regarding electric shavers — one who sees a clean-shaven man assumes that he shaved with a machine and not with a razor, since the permission is widespread, and there is no reason to shave with a razor when one can shave with a machine and get the same result.

Best regards,