You are spot on in implying that priests who can't sing are a relatively modern phenomenon. Many are the historic attestations that 'nothing has been said, but everywhere all has been sung since the beginning' (Simeon of Thessolonika, XIth cent.), which means that there was no such oddity as a priest who couldn't wouldn't sing until well into the middle ages. The middle ages saw a new phenomenon in the western Church, namely, the proliferation of monk-priests, all of whom needed to 'say' their daily masses in addition to participating in the conventual high mass. This led in the mediaeval era to the proliferation of essentially private masses at a surfeit of side altars. This was the origin of the so-called low mass, and it represents a sharp, and cruel, break with what was standard for over a thousand years in the western Church and still is in the eastern Churches, the totally chanted public mass.

To this day the Orthodox will not ordain a man who cannot sing, nor do they know of any such an historical eccentricity as a 'said' mass. Not only have we in the west grown accustomed to the so called low mass, quite a large number of people actually prefer it and are antipathetic to the fully chanted mass. There is a pathetically widespread acceptance of the development that not only do most priests no longer sing, but, in addition, it would never enter anyone's mind that they should.

What goes for priests goes, as well, for deacons. In fact, we have a gentleman PhD at Walsingham who is an instituted acolyte, a highly respected scholar of literature, Church history, and ritual matters who answers when asked why he doesn't become a deacon that he can't sing and therefore would not become a deacon because he couldn't sing his parts at mass at Walsingham. Alas! Would that more men were as respectful and conscientious of the ritual requirements of deaconhood - and priesthood.

It is human nature to sing when addressing God, or when engaged in religious ritual. Modern (since the late middle ages) Catholicism is unique in human history in presuming to worship its deity with the spoken voice rather than with ritual chant. It has this in common with western Protestantism, in which spoken worship is an historically cultivated tradition which was begun in conscious opposition to those old chanting Catholics. How 'Protestant' the Catholic Church has become in this regard!

The greater one's joy, the more profound the respect one has for another person, the more one's language takes on the aspect of musicality. The less another person is regarded, the less one's sense of well being and gladness, the less one's speech becomes musically expressive.

You have your good ones and you have your bad ones. I know of a local deacon who was informing an RCIA class that he didn't believe in praying to the saints because "they were all sinners, since we're all sinners." On the other hand, I was showing off my Liber to the chant group neophytes on campus (a rare occasion that) and one of the girls commented on how her father, a deacon in the St. Louis Archdiocese, would be "nerding out" over all of this, and how he was always trying to teach his fellow deacons how to chant.

The link above leads me to a page claiming "no ebook available" but in fact there is this.
In 1920 most priests would have been through seminary before TLS, and I think while the Pustet editions were still the approved chant style.