There aren't rules against it. Composers are encouraged to compose. On the other hand, music directors have the task of choosing suitable music.

There are good reasons not to use original Mass settings in a school, though. There are two important objectives to keep in mind. You want to prepare children to participate actively in the parish Sunday Mass, and you want the children to develop some experience with the Catholic musical heritage. So for a few months, they should learn a Mass setting used at the parish Sunday Mass, and then for a few months a setting from the chant repertoire.

Here's the USCCB official text from the GIRM:

393. Bearing in mind the important place that singing has in a celebration as a necessary or integral part of the Liturgy, all musical settings for the texts of the Ordinary of Mass, for the people’s responses and acclamations, and for the special rites that occur in the course of the liturgical year must be submitted to the Secretariat of Divine Worship of the United States Conference of Catholic Bishops for review and approval prior to publication.

While the organ is to be accorded pride of place, other wind, stringed, or percussion instruments may be admitted into divine worship in the Dioceses of the United States of America, according to longstanding local usage, in so far as these are truly suitable for sacred use, or can be made suitable.

So, what does "publication" mean? Does that mean that we can write our own musical setting of the Ordinary, Responsorial Psalm, etc. and use it as long as it isn't published by an official publisher?

As well as Mass of Creation 3.0 ;)

Here's an excerpt from the 2012 book Let Us Pray. The author (Fr. Turner) seems to be ignorant of recent legislation on the matter in question:

139. Finally, the option frequently taken by many parishes in the United States is “another liturgical chant that is suited to the sacred action, the day, or the time of year, similarly approved by the Conference of Bishops or the Diocesan Bishop” (GIRM 48). This option allows singing from the broadest repertoire of liturgical music. It would not support the singing of secular love songs at weddings. When choosing the text and music for the entrance chant, the appropriate song will be one that helps introduce the thoughts of the faithful “to the mystery of the liturgical time or festivity” (47).

140. The approval of local bishops in the third and fourth options can be formal, but commonly bishops have given at least tacit approval to the use of songs appearing in published worship aids, if not songs composed by local musicians. In 1996 the Bishops’ Committee on the Liturgy said of music in the United States, “No official approbation is required for hymns, songs, and acclamations written for the assembly,*1 provided they are not sung settings of the liturgical texts of the Order of Mass” (Committee on the Liturgy Newsletter 33 [January/February 1997] 5). Nonetheless, the GIRM gives conferences of bishops and diocesan bishops the authority to restrict the music to be sung in parishes. It is hard to imagine a conference of bishops ratifying the contents of a hymnal song by song, culture by culture, but they have the authority to do so.

Paul Turner serves as a facilitator for the International Commission on English in the Liturgy.

I'm pretty much convinced that neither such list will ever see the light of day in any of our lifetimes, if ever, both here and abroad. I wish I could be more optimistic that exhortations from the likes of B16 down through a Burke and then Wadsworth to Keyes to us would gain traction in the US conference alone. But the passing of generations, combined with the "Young and the Restless," will make headway.
What could be a cultural game-changer that (perversely) might work like it did in the advent of early American filmakers, might be some blockbuster film culled from a sort of positive message version of a RCC "Da Vinci Code" in which the glories of our tradition are an integral part of a barnburner script, where the camerlengo actually IS a hero. Or some such. I believe films like "The Way" achieve enough cult success to show that people want the mysteries and rituals to point them to inner transformation that they're willing to "buy into."
I don't know if I've articulated this vision well enough. Megaliturgies, even if a World Youth Event uses only Latin Rite chants, can never be "sold" as an option that the folks will slap their heads and exclaim, "Oh, that's how it should be." They, the BIG THEY, need a huge visceral experience, like a colloquium Requiem in IMAX, but also with the hook of a good yarn that speaks to their souls through the entertainment meets art medium.

especially composers of centuries past (The body of Gregorian Chant, Palestrina, Bach, Barber, Ockegem, Byrd, etc.

Wow, brother Samuel, you've come a long, long way.

To some extent Barber does indeed imitate tradition, but, in terms of sacred music, there is very little to assess. Most know of his sublime "Agnus Dei," which is an adaptation for unaccompanied chorus of music originally forming the slow movement of a string quartet and then later recast as the "Adagio for String." Much less well-known, but quite interesting, is his cantata "Prayers of Kierkegaard," which I have actually sung and whose lovely concluding chorale "Hold not our sins up against us" is something that I used several times as a choir director.

Don't get me wrong ... I love Sam Barber's music ... but I just don't think there is enough of his sacred opus to put it in the class of the others on Francis's list.

It is difficult, perhaps, to find a (deceased) 20th century/modern composer who might fit in that tradition worth emulating. But, to my mind, the sacred music of Ralph Vaughan Williams offers a larger and excellent body of sacred music to emulate, not just his many solid hymn settings, but also his "Mass in G minor," the cantatas "Dona nobis pacem" and "Hodie," plus the song-cycle "Five Mystical Songs."

ok... you can add your own 20th century composers... the rules still work.

Wendi- I'm pretty sure that this is actually accurate.
(Someone with doc-knowledge able to back that up?)

And from a practical standpoint, it makes perfect sense. Are you going to bother your Bishop every time you want to "try out" a new composition? You have to figure out if things work before you know if they are worth publishing.

W, I think I said something like this to you at SLC: The entity we call "The Church," being the longest, most successful political organization on the planet, manages quite easily to speak from both sides of an equation (or the corners of the mouth) simulaneously. So the question of "intent" regarding implementing specific musical compositions depends on who's heaviest on either end of the teeter totter. If you hear James Moore's TASTE AND SEE at a papal Mass in Australia, the Church encourages that form of expression. If Nicolai Montani starts a hymnal project in the 19th century while blacklisting, with St. Cecilia Society sanction authority from said hymnal formerly well accepted and ensconsed composers, then the Church tacitly encourages musical tyranny. One could go on with this duplicity ad infinitum and nauseum.
You know I manage four parish music ministry schedules. I know, for a fact, that at certain Masses, musical competency is so poor that it should be shuttered. But I haven't got any personnel to slot should I dismiss ANYONE. And, yes as you'd imagine, I do hold remediation sessions. OTOH, I have a retired priest in residence whose animus for one of the more talented singers and coros has prompted him to stop the singing of "La Gloria" mid-hymn to rant and rave and embarrass these generous volunteers (the maestra and organist are both former music students of mine in public HS choral.)
There's no magic bullet about what happens in our home turfs, so why would we think that there's a magic line in the sand the Church would draw about musical and compositional praxis on a universal, global level. Encourage/Discourage? Flip a coin. Kinda sad, really.

139. Finally, the option frequently taken by many parishes in the United States is “another liturgical chant that is suited to the sacred action, the day, or the time of year, similarly approved by the Conference of Bishops or the Diocesan Bishop” (GIRM 48). This option allows singing from the broadest repertoire of liturgical music. It would not support the singing of secular love songs at weddings. When choosing the text and music for the entrance chant, the appropriate song will be one that helps introduce the thoughts of the faithful “to the mystery of the liturgical time or festivity” (47).

140. The approval of local bishops in the third and fourth options can be formal, but commonly bishops have given at least tacit approval to the use of songs appearing in published worship aids, if not songs composed by local musicians. In 1996 the Bishops’ Committee on the Liturgy said of music in the United States, “No official approbation is required for hymns, songs, and acclamations written for the assembly,*1 provided they are not sung settings of the liturgical texts of the Order of Mass” (Committee on the Liturgy Newsletter 33 [January/February 1997] 5). Nonetheless, the GIRM gives conferences of bishops and diocesan bishops the authority to restrict the music to be sung in parishes. It is hard to imagine a conference of bishops ratifying the contents of a hymnal song by song, culture by culture, but they have the authority to do so.

I find this a remarkable statement. I hardly know what to make of it !!!

“No official approbation is required for hymns, songs, and acclamations written for the assembly,*1 provided they are not sung settings of the liturgical texts of the Order of Mass” (Committee on the Liturgy Newsletter 33 [January/February 1997] 5). Nonetheless, the GIRM gives conferences of bishops and diocesan bishops the authority to restrict the music to be sung in parishes. It is hard to imagine a conference of bishops ratifying the contents of a hymnal song by song, culture by culture, but they have the authority to do so.

Richard, if that isn't forked-tongued gobbledygook, then I am Ryan Gosling.

What exactly ARE considered the liturgical texts of the order of the Mass?

"Taaaaayyyyyyyssssssst and seeeeeeeeeeeeee.....etc."
Oh, and you, RC, just turned me into Ryan Gosling. Ladies, be gentle in the queue.
And Chonak generally turns me into a newt.

So...approval is necessary before using a Mass Setting? SIGH.

Andrew...tee hee...loved that movie. And thanks. I'm still kind of tentative about what I think I know.

Melo...thank you. for your answer. and... For being you.

sadly you are correct marajoy.