Answer

Hello Jonathan. A short question, but a long answer.
 
I should preface that I am writing this off the cuff, and not as a practical halakhic ruling. I haven’t checked enough. If this is a practical question, please tell me and I’ll examine it more carefully. Here I’m writing only what occurs to me at the moment for the sake of study alone.
 
It seems that fundamentally this depends on two points:
1. Is a woman obligated in prayer the way men are? (Because one who is not obligated in a matter cannot discharge others of their obligation.) The Mishnah in Berakhot indicates that she is. I think that according to most opinions this is also the halakhic conclusion. Prayer, according to Maimonides, is a Torah-level obligation and has no fixed time, and prayer that is time-dependent is rabbinic, and regarding rabbinic positive time-bound commandments many hold that women are obligated. And the Mishnah Berurah wrote that even according to the views that exempt them, they obligated women in prayer because prayer is a matter of asking for mercy—and one must consider whether this is a different obligation from that of men. Intuitively it would not seem so.
2. Does she count toward a minyan? (Because one who does not count toward the minyan cannot be the prayer leader.) Here the accepted practice is that she does not, but that is only because of considerations of the dignity of the congregation or modesty, which in my opinion are not relevant today. And it requires further examination whether the principle “when the reason lapses, the enactment does not lapse” applies here, or whether there is no enactment here at all, only a custom that developed because of modesty and the dignity of the congregation.
Therefore, strictly speaking, there is substantial room to say that a woman can also serve as prayer leader. But it is hard to permit something whose prohibition has become so deeply rooted that permitting it would seem truly astonishing (and Reform, God forbid). In any case, if I found myself in a place where a woman was serving as prayer leader, I would pray with them (that is, during her repetition of the Amidah I would read Shev Shma'tata and thereby intend to fulfill the commandment of Torah study).
 
However, you also asked about Musaf, and it seemed to me logically that there the situation might be different. And indeed I found that Rabbi Akiva Eiger brings in the name of Besamim Rosh (the known forgery 🙂 ) that the obligation of prayer depends on the obligation of the sacrifice, and women have no share in the sacrifice because they are not obligated in the half-shekel contribution. A bit over-pilpulistic, lacking basis, and in my opinion implausible, and it can easily be rejected. Had Rabbi Akiva Eiger known it was a forgery, perhaps he too would not have written this. However, the Tzelach wrote that women are not connected to the sacrifice because it is a positive time-bound commandment, and that seems more plausible. Therefore, regarding Musaf I would not permit such a thing.
 
And regarding the Shema, again there is room for discussion, since women are exempt from it. But with respect to the blessings of the Shema, the medieval authorities discussed whether they are part of the prayer liturgy or blessings on the Shema itself. (And regarding Ahavah Rabbah, some see it as including the blessings over Torah study, and women are obligated in the blessings over Torah study, as ruled by the Shulchan Arukh.) If so, here too women are not necessarily obligated. But I think that with the blessings of the Shema the question doesn’t really arise, because there is no special status there for a prayer leader. The blessings of the Shema are recited even by an individual, and I think that saying them together is only because of "in the multitude of the people is the King’s glory."
 
I repeat that I have not studied this sufficiently, and I hope I haven’t missed something. If this is a practical halakhic question, please tell me, because in that case I need to investigate much more carefully.
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A.:
In honor of Rabbi Michael Abraham,
       Following what you wrote regarding women receiving aliyot, please see the attached article:
https://drive.google.com/open?id=0BwJAdMjYRm7IQmM1N2JSYkRlejg
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Rabbi:
Thank you for the article (which was familiar to me, at least in part, and I had quite a few comments on it).
I just went through it again quickly from one end to the other, and I saw that it is good. Although of course there is a great deal to analyze in the discussion, as is the way of Torah, I’ll note here only a few comments (and again, I hope I’ll be forgiven if I erred, because I went through it very quickly):
1. It seems to me that at least in some cases, the halakhic decisors who hold that women are exempt from the Torah reading do not say so prior to the consideration of the dignity of the congregation, but because of that very consideration itself. If so, then according to their approach the conclusion could come out differently. (For if the consideration of the dignity of the congregation falls away—and of course that too requires discussion—then the obligation itself returns.) This is what I wondered about in the words of the Mishnah Berurah, who brings the Magen Avraham and does not cite dissenters, yet still comments that nowadays many did not follow him, and women also practiced fulfilling their obligation by hearing it. That implies there is no principled dispute here, only a lack of insistence on implementing their obligation due to some secondary consideration (the dignity of the congregation??). Still, it requires further examination why they should fulfill it if they are not obligated. Is there some prohibition in it?! I haven’t checked this now.
Be that as it may, regarding an aliyah and even the blessing, there is much room to permit even if women themselves are not obligated in the reading, as is written in the article.
2. The Rashba’s statement that you cited—that in a public setting anyone can read, even someone who is not obligated—should be expanded further. As a preface: with commandments that are imposed on the community, women too are obligated as part of the community, even if these are commandments from which they would otherwise have been exempt (for example, because they are time-bound, as with Hakhel, as implied in Sefer HaChinukh and elsewhere). Therefore perhaps with Torah reading too—and even if one understands it as part of the law of Torah study, something that itself is very doubtful in my opinion for several reasons—since it is communal Torah study, women are included in it. And then it would follow that even fundamentally they are actually obligated in it, and not only able to receive an aliyah and recite the blessing.
3. I would further note that regarding the dignity of the congregation, if I understood correctly (I read very quickly), the article discusses mainly two claims: 1. Whether it can be waived. 2. Whether human dignity overrides it (Sperber’s argument). But a third argument can also be raised: 3. Nowadays, in our current situation, there is no problem at all of the dignity of the congregation, because the congregation’s dignity is not harmed when women read or receive aliyot. And perhaps the opposite: when they do not receive aliyot, that is a blow to the dignity of the congregation. This of course depends on the question of what exactly “the dignity of the congregation” means, and this is not the place to elaborate.
4. I would add that even if the medieval authorities and halakhic decisors explain the term “the dignity of the congregation” in a certain way, in the final analysis the law still depends on whether in practice the congregation’s dignity is actually harmed or not. For example, even if someone explains that the congregation’s dignity is harmed if someone not obligated receives an aliyah, and even if we assume that women really are not obligated in the matter, one still must discuss the law when, in actual fact, the congregation’s dignity is not harmed by this (or at least that is how it is perceived today). Is that exactly like a congregation waiving its dignity, and therefore dependent on whether a congregation can waive it or not (as discussed in the article)? Or perhaps the claim that it cannot be waived applies only where in most cases the congregation does in fact see this as an affront to its dignity, and then there are opinions that even if a specific congregation wants to waive it, it cannot. But here, where reality has changed and in all congregations (at least the modern ones) it is not seen as an affront, then according to all opinions there is no problem of the dignity of the congregation, and it does not depend on whether a congregation can waive it or not. Put differently: the question is whether the halakhic decisors’ determination that this is not the dignity of the congregation is factual or normative.

There is also a related question here.

Thanks again,
Michi
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Tuvia:
There is some confusion here, in my humble opinion. A woman certainly does not count toward a minyan, not because of “the dignity of the congregation,” but by force of a scriptural derivation learned from the spies. Along with that, one could imagine that she could be a prayer leader even though she does not count toward the minyan, just as she may fundamentally receive an aliyah to the Torah even though she does not count among the ten without whom there is no Torah reading.

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Rabbi:
Indeed, there was a confusion. That was said about the quorum of seven. Regarding being counted toward a minyan of ten, see what I wrote here.