Ah, and here's the elephant in the room. Pius XII completely contradicted St. Pius X on this matter, proving once again how he was the WATERSHED transitional Pope into Vatican II. Whether it was this, or the Bugnini experimentations, or the condemnation of Father Feeney, or the promotion of NFP and of evolution, Pius XII contributed mightily to the Church's deline into full-blown modernism.
St. Pius X declared that by the very nature of liturgical office, being as it was clerical and therefore ultimately an extension of Holy Orders, choirs in Solemn Mass could not admit of women. So did the nature of the Liturgy change by the time of Pius XII that this would be permitted?
I for one, if I were pope, would require that those who exercise these functions / offices be given the appropriate MINOR ORDER for these things. In the Eastern Rite, you have CANTOR; in the Western Rite, you have LECTOR ... both essentially being the same minor order. Similarly, altar boys should ascend the steps should be in the MINOR ORDER of acolyte; whereas others in the sanctuary should be at least PORTERS.
At some point we lost the meaning of the minor orders and turned them into mere rituals, empty rituals, on the way to the Priesthood. I say empty rituals because even though, for instance, only the Lector should be able to chant the Epistle at Mass, any cleric was suddenly allowed to do so, etc. -- rendering the order of Lector hollow and meaningless.
And this transitions to Vatican II because these "offices" then really becomes just FUNCTIONS (aka "Ministries" as V2 calls them) rather than as extensions of Holy Orders.
With that said, I could see women / girls perhaps singing chant, etc. ... under certain circuмstances, during a Missa Cantata, since the Missa Cantata is not technically a Solemn Mass but rather a Low Mass, and the singing would just be for aesthetic purposes and not have an actual direct liturgical role in the Mass ... provided that all the responses were actually made by the altar server, which would be the actual official liturgical responses, while the singing would serve as window dressing. That's a VERY IMPORTANT distinction.
This isn't about men or women per se but about LITURGICAL THEOLOGY, and admitting women to sing during Solemn Mass is a major shift in LITURGICAL THEOLOGY that leads to concepts in the Novus Ordo Missae wherein various actions are no longer properly liturgical but just "functions" and "ministries" (services). Nor is it about some "concupiscence" thing to which Pius XII alludes by requiring that men and women be separated in choirs.