Let's take the 1917 Code as our final word on the matter. Church's mind is that it's indeed "desirable" ... per the reasons stated by the Church Fathers. Nevertheless, the Church has not mandated this, and Matthew points out the many practical considerations that militate against this ideal.
As for women in choirs, the issue is not primarily about modesty, but about the notion that singing the LITURGICAL chant is the same thing as a server saying the responses at Mass. Those are official liturgical prayers, at least in a SOLEMN High Mass, where the priest doesn't even say certain parts but defers to the choir. Consequently, as a liturgical function, it must be a clerical act, and it should no more be allowed than to have altar girls. [I'm actually in favor of requiring altar servers to receive minor orders based on the function they have in the liturgy.] In the Eastern Rite there's a minor order "Cantor" (just "Lector" in Latin Rite) for this very reason. Those minor orders are not symbolic, but they have become reduced to that, right? I think that we've lost the original meaning of the Minor Orders. Now, in the case of a simple Missa Cantata, however, the singing is meant simply for the edification of the congregation and is not strictly liturgical, as the priest continues to recite and the altar boys respond to the OFFICIAL LITURGICAL version. In that case, the singing of the chant is no different than if the choir were singing "Hail Holy Queen" or some other non-liturgical hymn.